Rigid body cable for virtual environments(多体动力学)
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EASILY TRANSPORTED from classroom toclassroom or to a recruitment event or openhouse. The VRTEX Mobile can be ready to goin a matter of minutes.BLENDED TRAINING SOLUTIONS FOR WELDING EDUCATIONTOUCHSCREEN USER INTERACTION providesequipment and procedural set-up on an intuitive,resistive touchscreen. All screens mirror theVRTEX 360, making transfer of interactionseamless between the systems.UNIVERSAL GUN HANDLE allows for connectionof a MIG/MAG gun attachment for GMAW andFCAW, and a stick attachment for SMAW welding.TABLETOP COUPON STAND easily attaches andstands on a standard table for welding and istaken apart for quick and simple storage insidethe VRTEX Mobile.The VRTEX systems are virtual reality arc welding training simulators. Thesecomputer based training systems are educational tools designed to supplementand enhance traditional welding training. They allow students to practice theirwelding technique in a simulated and immersive environment. The VRTEX systemspromote the efficient transfer of quality welding skills and body positioning tothe welding booth while reducing material waste associated with traditionalwelding training. The combination of realistic puddle, arc welding sound, andreal-time feedback tied to the welder’s movement provides a realistic andexciting, hands-on training experience.The VRTEX® Mobile is a basic, entry level welding training system. It is designedto provide mobility in an easy to use and engaging welding training tool. TheVRTEX Mobile is ideal for initial, basic welding training, as a recruitment andengagement tool for educational and industry and for employment and screeningfor human resources or as an evaluation tool for instructors and educators to geta baseline on student knowledge. The VRTEX Mobile is definitely on the move!VRTEX MOBILE PROVIDES:FLEXIBILITY» M ultiple welding processes and positions» V ariety of joint configurations» I nstructor tools allow modification basedon preferred welding program and styleINNOVATION» R ealistic welding puddle appearance and sounds» M agnetic tracking system provides accuratemeasurements for student score and evaluation» V irtual weld discontinuities appear in the weldwhen improper welding technique is usedCLASSROOM PERFORMANCE» Visual cues give real-time technique feedback» Advanced scoring system for student evaluation» E ncourages interaction — the instructor cancoach the welder while conducting virtualweld inspection» R ecord, archive and verify student work.CONSUMABLE ANDENVIRONMENTAL SAVINGS» No welding consumables, wire or waste» Track savings with the Weldometer™LANGUAGE SUPPORTEnglish, French, German, Spanish, Turkish,Japanese, Chinese (Mandarin), Portuguese(Brazilian), Russian, Korean, Hindi and ArabicDEMO MODE:Allows the instructor or student to view anexample weld or a demonstration of propertechnique, prior to a weld being madeREPLAY MODEAllows for instructor or student to reviewand analyze the welding processSET-UP AND INSTALLATION REQUIREMENTS:• T he VRTEX system requires minimal space for set-up. Dimensions are 8 W x 8 D x 8 H ft. (2.4 x 2.4 x 2.4 m).• W hen operating multiple units in one location, switch between standard and alternate frequency systems (unique part numbers are identified).• T he VRTEX Mobile system is not designed for operation in harsh environments. Recommendations are listed in the instruction manual.• A void magnetic fields, conductive and high frequency objects and processes.• A n uninterruptible power supply (UPS) may be required for protection of the system from power irregularities and/or disruptions.MC12-93 (06/15) © Lincoln Global, Inc. All Rights Reserved. Printed in U.S.A.CUSTOMER ASSISTANCE POLICYThe business of The Lincoln Electric Company is manufacturing and selling high quality welding equipment, consumables, and cutting equipment. Our challenge is to meet the needs of our customers and to exceed their expectations. On occasion, purchasers may ask Lincoln Electric for information or advice about their use of our products. Our employees respond to inquiries to the best of their ability based on information provided to them by the customers and the knowledge they may have concerning the application. Our employees, however, are not in a position to verify the information provided or to evaluate the engineering requirements for the particular weldment. Accordingly, Lincoln Electric does not warrant or guarantee or assume any liability with respect to such information or advice. Moreover, the provision of such information or advice does not create, expand, or alter any warranty on our products. Any express or implied warranty that might arise from the information or advice, including any implied warranty of merchantability or any warranty of fitness for any customers’ particular purpose is specifically disclaimed.Lincoln Electric is a responsive manufacturer, but the selection and use of specific products sold by Lincoln Electric is solely within the control of, and remains the sole responsibility of the customer. Many variables beyond the control of Lincoln Electric affect the results obtained in applying these types of fabrication methods and service requirements.Subject to Change – This information is accurate to the best of our knowledge at the time of printing. Please refer to for anyupdated information.。
Assembly-Free XJGInstallation & Maintenance InformationPull body away from the conduit so that the locking feature becomes disengaged. Once disengaged, slide the body over the grounding springs with a clockwise motion (viewing XJG from the threadedreducer end) until the bushing is centered in the body. This will allow for telescoping movement in either direction, refer to picture on next page. With the locking feature disengaged ensure the reducer is tight to the body. Holding the body stationary, tighten the reducer until the body bottoms out inside the reducer.IF 1508 • 08/14 Copyright © 2014 Eaton’s Crouse-Hinds Business Page 1FIGURE 2 - DISENGAGEDLocking feature is exposedFIGURE 1 - FULLy ENGAGEDLocking feature is not exposedAPPLICATIONXJG Expansion Joints are used with rigid metal conduit, IMC and withEMT conduit (when ordered with - EMT suffix), to couple together (2) two sections of conduit subject to longitudinal movement. XJG expansion joints are installed:• in long conduit runs to permit linear movement caused by thermal expansion and contraction.• in long conduit runs to prevent conduit from buckling and ensuing circuit failures.• indoors or outdoors where conduit expansion occurs and where there is a wide temperature range.These expansion joints are UL Listed (UL Std. 514B) and CSA Certified (CSA Standard 22.2-18) as an effective grounding means (i.e., the path to ground is permanent and continuous), for telescoping sections of conduit. They are also weatherproof and approved for use indoors or outdoors without an external bonding jumper. The internal grounding method provides excellent electrical continuity between the telescoping conduit, body and fixed conduit. XJG expansion joints meet the requirements of the National Electrical Code and Canadian Electric Code, providing an electrically continuous raceway; with no additional bonding means required. Multiple XJG assemblies are recommended in long conduit runs subject to extreme temperature fluctuations.XJG expansion joints permit conduit to telescope 2” in either direction for a total conduit movement of 4” (XJG4 Series); or 4” in either direction for a total conduit movement of 8” (XJG8 Series).XJG OVERVIEWReducerBushingBodyGland NutLocking FeatureGrounding Spring (2 Places)WasherPacking RingFiber GasketThe square locking feature as shown here can be found on tradesizes 1/2” - 1”. The remaining sizes will have the pin type as shown in subsequent figures. LOCkING FEATUREEaton’s Crouse-Hinds Business IF 1508 1201 Wolf Street, Syracuse, New York 13208 • U.S.A. R evision 4 Copyright© 2014 Revised 08/14 S upercedes 01/12All statements, technical information and recommendations contained herein are based on information and tests we believe to be reliable. The accuracy or completeness thereof are not guaranteed. In accordance with Cruse-Hinds “Terms and Conditions of Sale”, and since conditions of use are outside our control, the purchaser should determine the suitability of the product for his intended use and assumes all risk and liability whatsoever in connection therewith.Note: Tension between bushing and body is normal and necessary for proper grounding.Securely thread and tighten gland nut to compress packing ring onto conduit.Securely tighten second section of conduit into reducer.Ensure all connections are wrench-tight. Installation is complete. No external bonding jumper is required.INSTALLATION INSTRUCTIONS FOR EMT CONDUITDISASSEMBLy INSTRUCTIONS1. Remove conduit by unthreading conduit from reducer.2. Unthread and remove the gland nut, packing ring, fiber gasket and metalwasher from XJG body.3. Remove XJG body by pulling away from conduit with bushing stillthreaded to conduit.tighten until wrench-tight.Slide body with reducer over the ground springs with a clockwise motion.Fiber GasketPacking RingGland NutMetal WasherXJG BODYCenterNOTE - DO NOT DISASSEMBLEUse instructions below for original installation of product. If product is disassembled, or to reuse product, follow disassemly and EMT Gland NutReducerConduit NippleBodyCouplingEMT Connector BodyTO AVOID LOSS OF GROUND CONTINUITy,DO NOT REMOVE OUTER GROUND SPRINGS FROM BUSHING。
ABAQUS单元类型Advanced Finite Element Analysis–And ApplicationsDaming Zhang, Ph.D.Associate Professor of Transportation SystemsDepartment of Industrial TechnologyCollege of Agricultural Sciences and TechnologyCalifornia State University, FresnoMay 27, 2009Dr. Daming Zhang -Cal State Univ Fresno1Advanced Finite Element Analysis -And ApplicationsLecture 4:ABAQUS Element LibraryDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications2ABAQUS Elements OverviewA wide range of elements available for solving different problemsFive characteristics of an element:–Family–Degree of freedom–Number of nodes–Formulation–IntegrationUnique name: T2D2, S4R, C3D8Iused on the *ELEMENT option, TYPE parameterDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications3FamilyUsed to distinguish the geometryIndicated by first letter or letters: S4R, C3D8I, CINPE4 Dr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications4Degree of FreedomDegree of Freedom (DOF) are the fundamental variables 1Translation in direction 12Translation in direction 23Translation in direction 34Rotation about the 1-axis5Rotation about the 2-axis6Rotation about the 3-axis7Warping in open-section beam elements8Acoustic pressure or pore pressure9Electric potential11Temperature12+Temperature at other points through the thickness of beamsand shellsDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications5Number of Nodes ?Determines the interpolation orderfirst order, second order, …Clearly identified in the name: C3D8, S8RBeam family indicating order of interpolation: B31, B32 Dr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications6FormulationRefers to the mathematical theoryLagrangian:material descriptionEulerian:Spatial descriptionShell family has 3 classes:General purposethin-onlythick-onlyAlternative formulations (end of element name)Hybrid formulation: C3D8H, B31HIncompatible formulation: C3D8IDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications7IntegrationGaussian Quadrature to integrate quantities over the volume of each elementFull or Reduced integrationUse “R” at the end of element name to distinguish the reduced-integration elements: CAX4, CAX4RWill significantly affect the accuracyDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications8Continuum Elements (1)Used to model the widest variety of components ?Element names begin with “C”Next two indicate the dimensionality: 3D, PE, PS, AX ?The last shows the degree of freedom3D continuum elements:hexa, penta, tetra2D continuum elements:plane strainplane stressaxisymmetricshape: quadrilateralor triangularDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications 9Continuum Elements (2)2D continuum elements must be defined in 1-2 plane Node order should be counterclockwiseElement normals must all pointed at same direction ?Degree of freedom: translational DOFsElement properties: *SOLID SECTIONFormulation & Integration: Incompatible, Hybrid, Reduced ?Output variable: default in global coordinate system *ORIENTATION to define local coordinate systemDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications10Shell Elements (1)Used to model structure with one dimension small ?Element name begins with: S, SAX, SAXAThe first number indicates the number of nodesIf the last character is “5”, the element doesn’t use the rotational DOF around normal of middle plane ?Quadrilateral or triangular; Linear or quadratic elements ?Three different formulationsDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications 11Shell Elements (2)Degree of freedom: default 6 DOF, but also 5 DOF: S4R5 Axisymmetric shells have 3DOF:1Translation in the r-direction.2Translation in the z-direction.6Rotation in the r-z plane.*SHELL GENERAL SECTION: you define the properties*SHELL SECTION: ABAQUS calculates section properties ?Formulation & Integration: complicated, check before use ?Output variable: defined in the local material directions Lie on the surface of each shell elementAxes rotate with the element’s deformation in large-displacement simulationsDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications12Beam ElementsUsed to model structure with one dimension is quite large ?Element name begins with: B (e.g. B31)The first number indicates the dimensionalityThe third character indicates the interpolation order ?Degree of freedom: default 6 DOF, 2D beams have 3 DOF Open-section beams (e.g. B31OS) have DOF 7 for warping ?*BEAM GENERAL SECTION: you define the properties *BEAM SECTION: ABAQUS calculates section properties ?Formulation & Integration: Hybrid for very slender beams;B21, B31, B22, B32: shear deformable, and finite axial strain; B23 and B33 are not; Open section: B31OS, B32OS ?Output variable: axial stress (s 11), shear stress (s 12)Dr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications13Truss ElementsModel rods that can carry only tensile or compressive loads ?Element name begins with: T (e.g. T2D3, T3D2) The next two characters indicates the dimensionality ?Thefinal character indicates the number of nodes ?Degree of freedom: has only translational DOFs ?*SOLID SECTION: specify the material properties The cross-sectional area is given on the data line ?Formulation & Integration: Hybrid for very rigid links ?Output variable: Axial stress and strainDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications14Rigid ElementsElement name begins with: R (e.g. R3D4, R3D3)The next two characters indicates the dimensionality ?The final character indicates the number of nodes ?The nodes have no independent degrees of freedomThe nodes defining rigid elements can have loads applied to them or can be connected to other elements but they cannot have any boundary conditions ?*RIGID BODY defines the rigid body reference node ?Pay attention to the ‘sides’ of the rigid body elements ?Formulation & Integration: none ?Output: motion onlyDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications15Continuum Elements OverviewThe biggest family with over 20 just for 3D models ?3D: Hexa, Penta, Tetra; 2D: triangles and quadrilaterals ?Linear and quadratic versions for each of these shapes ?Full-and reduced-integration elements for hexa and quad ?Standard or hybrid element formulationFor linear hexa or quad: incompatible mode formulation ?For quadratic tria or tetra: "modified" formulationThe accuracy of your simulation will depend strongly on the type of element you use in your modelDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications 16Full IntegrationThe accuracy of Gaussian Quadrature is (2n-1) for n=4?The Element Stiffness Matrix is calculated by:Fully integrated linear elements use two integration points in each directionFully integrated quadratic elements use three integration points in each directionDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications 17k []m e=B []V ∫TD []B []dVFull Integration ExampleUse a cantilever beam to show the accuracy of analysisDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications 18Shear LockingHappened on fully integrated, first-order, solid elements causes the elements to be too stiff in bending ?Deformation of material subjected to bending moment MDeformation of a fully integrated, linear element Dr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications 19Reduced IntegrationOnly quadrilateral and hexahedral elements can use a reduced-integration schemeuse one fewer integration point in each direction than the fully integrated elementsDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications 20Reduced Integration ResultsLinear reduced-integration elements tend to be too flexible But fine mesh will produce acceptable results ?Deformation of a linear element with reduced integrationDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications21Incompatible mode elementsAn attempt to overcome the problems of shear locking in fully integrated first-order elementsAdditional degrees of freedom enhance the element's deformation gradients as linear variationcan produce results in bending problems that are comparable to quadratic elements but at significantly lower computational costThe mesh distortion should be minimized as much as possible to improve the accuracy of the resultsDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications22Hybrid ElementsHybrid elements have the letter "H" in their names ?Hybrid elements are used when the material behavior is incompressible (Poisson's ratio = 0.5)The volume cannot change if thematerial is incompressibleThe pressure stress cannot becomputed from the displacementsof the nodesHybrid elements include an additional degree of freedom that determines the pressure stress in the element directly Dr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications23Selecting Continuum ElementsUse quadratic, reduced-integration elements (CAX8R, CPE8R, CPS8R, C3D20R, etc.) for general analysis workUse quadratic, fully integrated elements (CAX8, CPE8, CPS8, C3D20, etc.) locally where stress concentrations may exist Use a fine mesh of linear, reduced-integration elements (CAX4R, CPE4R, CPS4R, C3D8R, etc.) for large-strain analysis For contact problems use a fine mesh of linear, reduced-integration elements or incompatible elements (CAX4I, CPE4I, CPS4I, C3D8I, etc.)?Minimize the mesh distortion as much as possibleIn three dimensions use hexahedral (brick-shaped) elements wherever possible; Use C3D6 and C3D4 only when necessary ?modified quadratic tetrahedral element (C3D10M) is robust for large-deformation and contact problems and exhibits minimal shear and volumetric lockingDr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications24Thank You Dr. Daming Zhang -Cal State Univ Fresno Advanced Finite Element Analysis -And Applications25。
Ordering detailsi n e (c d )²ConsumptionPictogramViewing distance Included labels12m, 20m or 30m4 Non-adhesive Exit legends (D,U,R,L) ISO format Luminous fl ux ΦE /ΦNat end of rated operating time 100% @ 1h, 50% @ 2h, 30% @ 3h, 16% @ 8hIllumination in mains mode 50 or 500 cd setting via switch,and possible additional setting via magnet (30%, 70%, 100%)OperationMaintained / Non-Maintained (via switch input)Duration Confi gurable 1/2/3/8 hoursTesting system Automatic Test in compliance with EN 62034Connection possible to the CGLine+ monitoring system HousingType of mounting Material Colour Wall surface-mounting Polycarbonate White RAL9003Degree of protection IP43 or IP66 / IK07TerminalsScrewless terminals for fl exible and rigid wires From 0,5 to 2,5 mm²Connection voltage220 - 240 V AC, 50/60 HzPermissible ambient temperature 5°C to 45°C, 0°C to 45°C in maintained mode. 35°C max for 10 years lifetime.Battery LiFePO4Light source LED, Lifespan 100 000h Insulation ClassIIFlexiTech EW 30m/20m/12m viewing distanceDimensions (mm)12m / 20m : 23130m : 32612m : 8620m : 12530m: 17812m / 20m : 3430m : 38FlexiTech EW CGLine+• Self-contained luminaire with Automatic Test and individual monitoring (CGLine+) for reduced inspection effort • Single sided exit sign with light guide technology for wall mounting• Robust construction IK07 for reliable operation even in difficult environments • Available with 12, 20 and 30m viewing distance and protection degrees IP43 and IP66• Non-obtrusive design and with a slim housing (34 / 38 mm)• Including inlay legends for commonly used configurations reducing the logistic effort to have the right pictograms on site • The inlay legends are well protected against scratches and dirt• Increased affordance functionality for better visibility of the exit sign and faster evacuation • O ptimal recognition via high luminance of white contrast colour > 500 cd/m2 according to DIN4844-1 / ISO 3864-1 (for bright surroundings), and perfect uniformity L min/L max > 0.8• Brightness selectable in two steps in mains operation (eg. theater: 50 cd/m², Supermarket: 500 cd/m²) and additional setting (30%, 70%, 100%)• Selectable operating time (1/2/3/8h operation)• Selectable operation mode (Maintained or Non-Maintained) via switch input• Fast installation and effortless wiring thanks to: cable entries in rubber, large space for cabling, screwless terminal blocks, integrated spirit level and first fixed base plate to snap on the housing without any tool • T ransparent base plate with honeycomb footprint for easy replacement of existing products (IP4x use only)• Low eco-footprint thanks to its eco-designed, low consumption and Lithium battery• Simple fault analysis and status display via bicolor LED, testing button (magnet) and supervision solutions • Lifespan: 10 years without component replacement, proven with 1 year aging test @70°C ambient temperature • Complete range of accessories (recess kit, wire guard)• Coloured accessories available on demand, custom designed pictograms also availableAccessories Black matRAL9005Dark GreyRAL7015Silver glossRAL9007FT1-RK Recess Kit for FlexiTech EW 12m FT1-RK-B FT1-RK-DG FT1-RK-SFT2-RK Recess Kit for FlexiTech EW 20m, metal FT2-RK-B FT2-RK-DG FT2-RK-SFT3-RK Recess Kit for FlexiTech EW 30m, metal FT3-RK-B FT3-RK-DG FT3-RK-SMetal cover for FlexiTech EW 12m FT1EWSU-MC-B FT1EWSU-MC-DG FT1EWSU-MC-SMetal cover for FlexiTech EW 20m FT2EWSU-MC-B FT2EWSU-MC-DG FT2EWSU-MC-SMetal cover for FlexiTech EW 30m FT3EWSU-MC-B FT3EWSU-MC-DG FT3EWSU-MC-S FT2-WG Wire Guard, compatible with FlexiTech EW 12m and 20mFT3-WG Wire Guard, compatible with FlexiTech EW 30mFT1-RB Recess box / plaster & brick for FlexiTech EW 12mEMN Eaton Magnet for confi guration and testsFT-BATLL1Battery LiFePO4 long life, 3,2V / 600mAhFT-BATLL2Battery LiFePO4 long life, 3,2V / 1500mAhFT1-4I Set of 4 pictos for FlexiTech EW, 12m (D, L, R, U), ISO formatFT2-4I Set of 4 pictos for FlexiTech EW, 20m (D, L, R, U), ISO formatFT3-4I Set of 4 pictos for FlexiTech EW, 30m (D, L, R, U), ISO formatPictogramsFT2EWEC-PICTO-VL FT3EWEC-PICTO-VL Picto, ISO7010-E001 VL, Exit Vertical LeftFT2EWEC-PICTO-VR FT3EWEC-PICTO-VR Picto, ISO7010-E002 VR, Exit Vertical RightFT2EWEC-PICTO-VD FT3EWEC-PICTO-VD Picto, ISO7010-E002 VD, Exit Vertical DownFT2EWEC-PICTO-UR FT3EWEC-PICTO-UR Picto, ISO7010-E002 U/R, Exit Up RightFT2EWEC-PICTO-DR FT3EWEC-PICTO-DR Picto, ISO7010-E002 D/R, Exit Down RightFT2EWEC-PICTO-DL FT3EWEC-PICTO-DL Picto, ISO7010-E001 D/L, Exit Down LeftFT2EWEC-PICTO-UL FT3EWEC-PICTO-UL Picto, ISO7010-E001 U/L, Exit Up LeftFT2EWEC-PICTO-DMD FT3EWEC-PICTO-DMD Picto, FDX08-040-3 T28, Man in wheelchair door & arrow downFT2EWEC-PICTO-DML FT3EWEC-PICTO-DML Picto, FDX08-040-3 T28, Man in wheelchair door & arrow leftFT2EWEC-PICTO-DMR FT3EWEC-PICTO-DMR Picto, FDX08-040-3 T28, Man in wheelchair door arrow rightFT2EWEC-PICTO-DMU FT3EWEC-PICTO-DMU Picto, FDX08-040-3 T28, Man in wheelchair door arrow upFT2EWEC-PICTO-DML1FT3EWEC-PICTO-DML1Picto, DIN4844, Man in wheelchair & arrow leftFT2EWEC-PICTO-DMR1FT3EWEC-PICTO-DMR1Picto, DIN4844, Man in wheelchair & arrow rightFT2EWEC-PICTO-DMD1FT3EWEC-PICTO-DMD1Picto, DIN4844, Man in wheelchair & arrow downFT2EWEC-PICTO-EWL FT3EWEC-PICTO-EWL Picto, ISO7010-E016, Escape Window LeftFT2EWEC-PICTO-EWR FT3EWEC-PICTO-EWR ISO7010-E016, Escape Window RightFT2EWEC-PICTO-EWD FT3EWEC-PICTO-EWD Picto, ISO7010-E016, Escape Window DownFT2EWEC-PICTO-RWL FT3EWEC-PICTO-RWL Picto, ISO7010-E017, Rescue Window LeftFT2EWEC-PICTO-RWR FT3EWEC-PICTO-RWR Picto, ISO7010-E017, Rescue Window RightFT2EWEC-PICTO-RWD FT3EWEC-PICTO-RWD Picto, ISO7010-E017, Rescue Window DownFT2EWEC-PICTO-MP FT3EWEC-PICTO-MP Picto, ISO7010-E007, Meeting PointFT2EWEC-PICTO-CR FT3EWEC-PICTO-CR Picto, ISO7010-E003, First-AidFT2EWEC-PICTO-H FT3EWEC-PICTO-H Picto, HydrantFT2EWEC-PICTO-FEX FT3EWEC-PICTO-FEX Picto, ISO7010-F001, Fire ExtinguisherFT2EWEC-PICTO-FHO FT3EWEC-PICTO-FHO Picto, ISO7010-F002, Fire HoseFT2EWEC-PICTO-INFO FT3EWEC-PICTO-INFO Picto, ISO7001/P-I PF001, INFOFT2EWEC-PICTO-WC FT3EWEC-PICTO-WC Picto, ISO7001/P-I PF003, WC。
立维腾混合技术动静感应器被授予ADEX白金奖
佚名
【期刊名称】《建筑电气》
【年(卷),期】2009(28)7
【摘要】2009年5月27日美国立维腾设计、生产的0SSMD—D动静感应器荣获美国设计杂志ADEX国际设计大赛最高奖——自金奖(卓越设计奖),本次奖项评判人员由建筑师、设计师和行业专家组成,吸引了来自全国各地厂商参加的,参选产品达1200款以上,获得此奖项的产品要求在建筑和室内设计市场上均具有卓越的设计及品质。
【总页数】1页(P15-15)
【关键词】感应器;混合技术;金;产品要求;设计师;设计市场;建筑师;美国
【正文语种】中文
【中图分类】TU2-24;TG155.24
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The new standard in RF impedance and material measurements.AgilentE4991A RF Impedance/Material AnalyzerTechnical Overviewand 801 sweep points.different multi-parameter models.- inch floppy disk drive andhard disk drive are available.Store VBA program, calibration data,2External VGA output•Display measurement results on alarger VGA monitor.External keyboard and mouse interface•VBA programming made easy.•Users can perform operations with amouse for more comfortable operation.USB interface•Control external instruments using the82357A USB/GPIB interface.•Support USB interface printers.Advanced Solution Array for RF Impedance and Material MeasurementThe E4991A provides a powerful tool for component manufacturingR&D engineers and circuit designers of wireless and digital equipment who want to evaluate components from various per-spectives. The following are application examples:Passive components•RF impedance measurementof chip components such asceramic capacitors, RFinductors, ferrite beads, andresistorsSemiconductors•Capacitance-Voltage (C-V)characteristics andEquivalent Series Resistance(ESR) measurements ofvaractor diodesMaterials•Permittivity and loss tangentevaluation of plastics,ceramics, printed circuitboards and other dielectricmaterial•Permeability and losstangent evaluation of ferrite,amorphous and othermagnetic materials3E4991A Provides New Insights into RF Passive Component Behavior Array The Agilent E4991A's enhanced frequency coverage up to 3 GHzis compatible with wireless communication applications such as W-CDMA, Bluetooth TM, and Wireless LAN. The E4991A’s wide impedance coverage and versatile measurement functions allow analysis of RF chip inductors and capacitors under actual operating conditions. A wide range of test fixturing solutions makes tiny chip device measurements even easier.Quality Factor (Q) and Equivalent Series Resistance (ESR) are critical parameters for the components used in mobile communication equipment. Q and ESR measurements require high accuracy. Prior to the E4991A, there was not a good solution available over 2 GHz. The E4991A offers much improved Q and ESR accuracy over traditional network analyzers; due to the enhanced RF I-V technique that measures voltage and current at the device under test (DUT), along with the innovative low-loss capacitor calibration.Table 3 provides a brief summary of the key differences between Agilent E4991A and networkanalyzers.4In-depth Device Array CharacterizationIntuitive graphical userinterfaceThe 8.4-inch color LCD withWindows-based GUI brings anintuitive view of measurementsettings and results. The E4991Acan display up to 3 scalarand 2 complex parameterssimultaneously.Figure 2 shows a measurementresult of a chip bead. You canobserve the |Z|, R and X parame-ters on the display at same time.You can also assign each measure-ment trace in a separate window.Windows-styled GUI brings theadded benefits of mouse operationto the E4991A. Simply drag themouse over the area you areinterested in and you can zoomin quickly and easily. (See Figure 3)5DC bias function–Option E4991A-001For components with voltage and current dependency, such as RF inductors or ceramic capacitors, the DC bias function (Option E4991A-001) supplies DC voltage (±40 V) and current bias (±50 mA)across the device. You can easily observe your device behavior under various DC bias conditions without using an external DC bias source. External DC bias adapter If you require even higher DCcurrent bias, the Agilent 16200B external DC bias adapter allows you to apply larger DC bias across the device of up to ±5 A through a 7-mm test port by using an external DC current source.E4991A operating frequencyis limited to 1 GHz with the 16200B.Extracting the equivalent circuit parametersThe equivalent circuit analysis function offers more detailed circuit models over the standard 2-parameter model. Five different multi-parameter models accom-modate different types of devices, such as ceramic capacitorsor crystal resonators. You can simulate the impedance trace of your own equivalent parameter values and then compare it with actual measurement traces. The extracted parameters can also be used with electronic design automation(EDA) tools to improve modeling accuracy.Figure 4 shows the C-Vcharacteristic measurementof a varactor diode. SweepingDC voltage from 0.5 V to 4.5 V,you can easily read capacitancechange (11.27 pF) using thedelta marker function. EvaluateDC bias voltage dependency oncomponents easily. DC currentbias measurement is also avail-able so that you can evaluatecharacteristics of inductors, suchas, saturation or hysteresis.Figure 4. Varactor diode capacitance vs. DCvoltage characteristicsFigure 5-1. 16200BFigure 5. 16200B DC bias adapter connected to the E4991AFigure 6. Equivalent circuit analysis models6Connectivity Advances with PC and Windows-basedTechnologyVisual Basic for applications (VBA) helps automate tasksThe built-in VBA is available for customization and automation of complex measurement procedures. You can create macro programs in the Integrated Development Environment (IDE) of VBA in a similar manner to Visual Basic®operation.Link to EDA toolsUsing electronic design applications such as Agilent’s Advanced Design System (ADS), in conjunction with the E4991A, can help you optimize and verify the performance of your device with simulated circuit modeling. You can easily store measured data in CITIFILE format and import to EDA software tools. (Agilent’s ADS software may be purchased separately from theE4991A.)LAN interface enables seamless connectivity with PC environmentUsing the remote user interface software provided with theE4991A, you can easily correct data and troubleshoot over the LAN interface. The remote user interface brings the instrument control panel to the PC display via LAN. You can gain controlof instruments in physically separate locations. Easily share your measurement data with other applications, such as spreadsheets, through a fileor via the clipboard.Figure 10. VBAFigure 11. ADS figureFigure 12. Remote user interface8Material Analysis Made EasyThe dielectric and magnetic measurement software(Option E4991A-002)provides direct readout of materialparameters such as permeability and permittivity up to 1 GHz. The dielectric material test fixture,16453A, and the magnetic material test fixture, 16454A, eliminate designing time-consuming custom test fixtures.Dielectric material testingThe 16453A employs the parallel plate method for dielectric constant and loss tangent measurements up to 1 GHz. It is well-suited for measuring a sheet of solid substrate material,such as PC board, ceramic or polymer. Simple measurements are possible by inserting the material between the electrodes.With E4991A Option E4991A-002,material measurement function,you can display permittivity parameters directly on the ana-lyzer’s display.Magnetic material testingThe 16454A is used for perme-ability measurements up to 1 GHz on the E4991A. This single-wound,coil-structured test fixture holds toroidal-shaped magnetic materials such as soft-ferrite and magnetic cores. It is possible to accommodate different sizes of toroidal cores by exchanging small (smaller than 8 mm diameter) and large adapters. To use the 16454A, you need the material measurement function (Option E4991A-002).9Material size requirementsDiameter ≥15 mm Thickness ≤3 mmMaterial size requirementsSmall size:Outer diameter ≤8 mm Inner diameter ≥3.1 mm Thickness ≤3 mmLarge size:Outer diameter ≤20 mm Inner diameter ≥5 mm Thickness ≤8.5 mmFigure 13. E4991A with material test fixturesFigure 14. 16453A Dielectric material fixtureFigure 15. 16454A Magnetic material fixtureEasy installationWhen connecting the E4991Ato probe stations, the accuracydegradation, caused by portextension and improper calibra-tion, always becomes a big issue.The Option E4991A-010 probestation connection kit, forE4991A provides all necessaryparts as one option and solvesthis problem. This optionincludes a smaller test head,extension cables, adapters, aconnecting plate and detailedinstallation procedures. Probestations are provided fromCascade Microtech, Inc. Withthis kit, you can easily establisha reliable measurement systemin the short time.Impedance measurementspecification at theextended test head portThe E4991A’s Option E4991A-010has a guaranteed impedancemeasurement specification atthe end of the extended 7-mmtest head port.This is an impor-tant element for accurate mea-surement, because the portextension usually de-grades themeasurement accuracy.The situa-tion becomes even worse if thecable used has an impropercharacteristic. Agilent solvedthis issue by preparing reliableextension cables andmaking a special test head. Thistest head is small enough to bebrought closer to probe stations,so that the measurement errorcaused by this extra length isalso minimized.Figure 16. Agilent E4991A with probe stationAccurate impedance measurement with probe stationFigure 17. Probe measurement configuration using E4991A Option E4991A-010Test head*Extension cable*E4991AMounting plate3.5-mm to 7-mmadapter**Comes with Agilent E4991A Option E4991A-010probe station connection kit.Semi-rigid cableDUTProbe headStage1011Wide and repeatable impedance measurementAgilent E4991A can cover wider impedance range than network analyzers. In general, network analyzers are good at measuring impedance near 50 Ω, but the accuracy gets worse forimpedance away from 50 Ω. The E4991A is designed to measure non-50 Ωimpedance as well, so it can give much better accuracy especially when you measure small capacitance and inductance like 1 pF and 1 nH. The E4991A is repeatable over time andtemperature, too This is another benefit of dedicated impedance analyzers.Figure 18. Agilent E4991A Option E4991A-010 probe station connection kitWhat is E4991A Option E4991A-010The E4991A Option E4991A-010includes following items:• Smaller E4991A test head • Extension cables• 7mm - 3.5mm (f) adapter x 1 ea.• N (m)-SMA(f) adapter x 3 ea.• Installation manualProbeanalyzerWhat else do you need for a system?Besides the E4991A with Option E4991A-010, a probe station and probe heads need to be purchased separately. This option works with any probe stations, but we recommend Cascade Microtech probe sta-tions, because this combination was carefully checked to work well. The following are product examples:• Summit 9000, 11000, or 12000series probe station• ACP-series or HPC-series probe head• Impedance Standard Substrate (ISS)• Adjustable mounting plate for the E4991A test head.• Semi-rigid cable for the probe head connectionThese products are provided by Cascade Microtech, Inc.High-temperature cablestationprogram12The temperature characteristic test kit, E4991A Option E4991A-007, is a new solution of temper-ature characteristic measurement for components and materials.This solution provides highly accurate temperature character-istic analysis capability within the wide temperature range from -55°C to +150°C with a powerful temperature drift compensation function.Figure 19 shows the typical 10%measurement accuracy range of the E4991A compared to the 4291B. The 4291B requires both low and high impedance test heads for obtaining the wide impedance measurement range.On the other hand, the E4991A covers the wider impedance measurement range with a single test head.The temperature drift compensa-tion function is a new technology that is adopted in the E4991A.Unlike the 4291B, open/short compensation can be performed at pre-defined temperature points so that temperature drift errors can be drastically reduced as shown in Figure 20.Easy integration with the ESPEC 1temperature chamberESPEC supplies a temperature chamber, while Agilent provides all other necessary accessories and a sample program for creat-ing an automated temperature characteristic test system. Figure 21 shows the contents of the E4991A Option E4991A-007.2A VBA sample program is compatible with the ESPECbench-top temperature chamber,SU-261, so that you can easily integrate an automated tempera-ture characteristic test system Figure 22. The SU-261 provides a wide temperature range from -60°C to +150°C; which covers the entire temperature range of Option E4991A-007. Also, this sample program can be modifiedto fit other companies’ tempera-ture chambers. In addition, theVBA sample program provides an intuitive GUI interface; which provides the temperature chamber control, measurement parameter setup, and temperature profilesetup with easy operation.Figure 19. Typical 10% measurement accuracy comparison chartFigure 20. Effect of the temperature drift compensation functionFigure 21. Contents of the E4991A Option E4991A-007Integrated Temperature Characteristic TestingA temperature characteristic test solution is now availableFigure 22. The E4991A Option E4991A-007 with the ESPEC bench-top temperature chamber (SU-261)1.ESPEC is an Agilent channel partner.2.The Agilent 82357A USB/GPIB interface is required to control the chamber from the E4991A. The USB/GPIB interface is not included in the Option E4991A-007.13<E> For manual2❑ E4991A-ABAU.S. - English localization❑ E4991A-ABJJapan - Japanese localization ❑ E4991A-0BW service manual Accessories316197A4 bottom electrode SMD test fixture (up to 3 GHz)Options16197A-001 add 0201 (inch)/0603 (mm) device guide set16197A-ABAU.S. - English localization16197A-ABJJapan - Japanese localization 16196A/B/C/D5parallel electrode SMD test fixture (up to 3 GHz) Options16196A/B/C/D-710 add magnifying lens and tweezers 16196A/B/C/D-ABJJapan - Japanese localization 16196A/B/C/D-ABAU.S. - English localization16196U maintenance kits for 16196X Options16196U-010 upper electrode set for 16196A/B/C (5 ea)16196U-020 upper electrode set for 16196D (5 ea)16196U-100 1608 (mm) short plate set (5 ea)16196U-110 1608 (mm) lower electrode set (5 ea)16196U-200 1005 (mm) short plate set (5 ea)16196U-210 1005 (mm) lower electrode set (5 ea)16196U-300 0603 (mm) short plate set (5 ea)16196U-310 0603 (mm) lower electrode set (5 ea)16196U-400 0402 (mm) short plate set (5 ea)16196U-410 0402 (mm) lower electrode set (5 ea)16191A6bottom electrode SMD test fixture (DC to 2 GHz)Options16191A-701 short bars set(1 x 1 x 2.4, 1.6 x 2.4 x 2,3.2 x 2.4 x 2.4,4.5 x 2.4 x 2.4) mm 16191A-710 add magnifying lens and tweezers16191A-010 EIA/EIAJ industry sized short bar set16192A6parallel electrode SMD test fixture (DC to 2 GHz)Options16192A-701 short bars set(1 x 1 x 2.4, 1.6 x 2.4 x 2,3.2 x 2.4 x 2.4,4.5 x 2.4 x 2.4) mm 16192A-710 add magnifying lens and tweezers16192A-010 EIA/EIAJ industry sized short bar set16094A probe test fixture(up to 125 MHz)16453A dielectric material test fixture (up to 1 GHz)16454A magnetic material test fixture (up to 1 GHz)16190B performance kit16195B 7-mm coaxial calibration kit 16092A SMD test fixture(up to 500 MHz)16200B external DC bias adapter (up to 1 GHz)82357A USB/GPIB Interface for Windows71. Test fixtures, a keyboard, a mouse, USB/GPIB Interface, and a printed manual are not furnished as standard.2.Printed manual is not furnished as standard.3. Additional accessory details can be found in the Accessories Selection Guide for Impedance Measurements, publication number 5965-4792E.4. Must specify one of language options (ABA or ABJ) for operation manual for shipment with product.5. Magnify lens and tweezers are not furnished as standard. Must specify one of language options (ABA or ABJ) for operation manual forshipment with product.6. Short bar set, magnify lens, and tweezers are not furnished as standard.7.The USB/GPIB Interface is required to control external devices.E4991A Configuration and Accessory Guide14/find/emailupdates Get the latest information on the products and applications you select.For Cascade Microtech products,contact Cascade Microtech, Inc.Cascade Microtech2430 NW 206th AvenueBeaverton, Oregon 97006, U.S.A.Tel. 503-610-1000Fax. 506-601-1002Email sales@For the ESPEC products, contactESPEC Corp.ESPEC CORP.3-5-6, Tenjinbashi, Kita-ku, Osaka,530-8550 JapanTel. +81-6-6358-4741Fax. +81-6-6358-5500www.espec.co.jpESPEC North America, Inc.425 Gordon Industrial Court, S.W.Byron Center, MI 49315-8354, U.S.A.Tel. 616-878-0270Toll Free 1-800-537-7320Fax. 616-878-0280Agilent Technologies’ Test and Measurement Support,Services, and AssistanceAgilent Technologies aims to maximize the value youreceive, while minimizing your risk and problems. 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Baseline finite element modeling of a large span cable-stayed bridge through field ambient vibration testsWei-Xin Rena,b,*,Xue-Lin PengaaDepartment of Civil Engineering,Fuzhou University,Fuzhou,Fujian Province 350002,PR ChinabDepartment of Civil Engineering,Central South University,Changsha,Hunan Province 410075,PR ChinaReceived 22May 2004;accepted 23November 2004Available online 12January 2005AbstractA baseline finite element model is a reference in structural damage detection and long-term health monitoring.An ambient vibration measurement based procedure is presented to develop such a baseline model for a newly constructed Qingzhou cable-stayed bridge over the Ming River,Fuzhou,China.A 605m main span of the bridge is currently the longest in the world among all completed composite-deck cable-stayed bridges.The procedure includes several tasks:finite element modeling,field ambient vibration testing,parametric studies and model validation.It is demonstrated that the ambient vibration measurements are enough to identify the most significant modes of large span cable-stayed bridges with a low range (0–1.0Hz)of natural frequencies of interest.Some important issues in the modeling of such a complicated bridge,such as the initial equilibrium configuration due to dead load,geometrical nonlinearities,concrete slab,the shear connection of the composite deck,and the longitudinal restraints of the end expansion joints,have been clarified.The developed three-dimensional finite element model of the bridge has achieved a good correlation with the measured natural frequencies and mode shapes identified from field ambient vibration tests.Ó2004Elsevier Ltd.All rights reserved.Keywords:Cable-stayed bridge;Finite element model;Baseline;Structural dynamics;Health monitoring;Ambient vibration test;Modal analysis;Cable tension1.IntroductionCivil infrastructures serve as the underpinnings of our present highly industrialized society.It is an impor-tant issue how to monitor these widely used infrastruc-tures in order to prevent potential catastrophic events.Bridges,a type of important civil infrastructures,are normally designed to have long life span.Service loads,environmental and accidental actions may cause damage to bridges.Continuous health monitoring or regular condition assessment of important bridges is necessary so that early identification and localization of any poten-tial damage can be made.The contemporary cable-stayed bridge is becoming more and more popular and being used where previ-ously a suspension bridge might have been chosen.The increasing popularity of cable-stayed bridges are0045-7949/$-see front matter Ó2004Elsevier Ltd.All rights reserved.doi:10.1016/pstruc.2004.11.013*Corresponding author.Address:Department of Civil Engineering,Fuzhou University,Fuzhou,Fujian Province 350002,PR China.Tel.:+8659187892454;fax:+8659183737442.E-mail address:ren@ (W.-X.Ren).URL:.Computers and Structures 83(2005)536–550/locate/compstrucattributed to,(1)the appealing aesthetics;(2)the full and efficient utilization of structural materials;(3)the in-creased stiffness over suspension bridges;and(4)the rel-atively small size of the bridge elements.Very large spans have been built,for examples,890m for Tartara bridge in Japan,856m for Pont de Normandie bridge in France,and628m for Nancha bridge in China. Cable-stayed bridges are now entering into new era, increasing a central span length to1000m or even longer.There have been several concerns over the use of cable-stayed bridges despite all the advantages.Cable-stayed bridges are apt to look somewhat angular and highly stressed.They are normally sensitive to dynamic loadings such as earthquakes,winds and vehicles.More-over,the health monitoring and condition assessment of large span cable-stayed bridges is a crucial issue to en-sure safety during the bridge service life.One way to carry out the health monitoring or structural assessment is through changes in vibration characteristics(natural frequencies,damping ratios,and mode shapes)of bridges.Those changes,if properly identified and classi-fied,can provide the means for assessing the damage of the structure[1].Due to the structural complexity of large span cable-stayed bridges,thefinite element(FE)method is cur-rently a common way to perform the modal analysis and dynamic response analysis under earthquake,wind and vehicle loadings[2–9].Starting from the knowledge of the structure geometry,the boundary conditions and material properties,the mass,stiffness and damping dis-tribution of the structure are expressed in a matrix form. To identify changes in the dynamic characteristics of a bridge,a baselinefinite element is often required.Bridge health can be monitored or assessed when the baseline model is compared against afinite element model of the updated bridge.However,the success offinite element method application strongly depends on the reliability of the model since many simplifying assump-tions are made in modeling the complicated structures, and there are many uncertainties in the material and geometric properties.The calculated results are often questionable if thefinite element model is not properly validated by thefield test results.Field dynamic testing of a bridge provides a direct way to estimate its dynamic characteristics.There are three main types of bridge dynamic tests:(1)forced vibration tests;(2)free vibration tests;and(3)ambient vibration tests.In the forced vibration method,the bridge is excited by artificial means and correlated in-put–output measurements are performed.In the case of large andflexible bridges,like cable-stayed bridges, it often requires very heavy equipment and involves sig-nificant resources to provide controlled excitation at suf-ficiently high levels[10],which becomes difficult and costly.Free vibration tests of bridges is carried out by a sudden release of a heavy load or mass appropriately connected to the bridge deck[11].Both forced and free vibration tests,however,need an artificial means to ex-cite the bridge,additionally traffic has to be shut down during the tests.Ambient vibration tests have an advantage of being inexpensive since no equipment is needed to excite the bridge.It corresponds to the real operating condition of the bridge.The service state need not have to be inter-rupted to use this technique.Ambient vibration tests have been successfully applied to several large scale cable-supported bridges[12–19].In case of ambient vibration tests,only response data are measured while actual loading conditions are not measured.A modal parameter identification procedure will therefore need to base itself on output-only data.In thefirst effort to carry out the long-term health monitoring on the Qingzhou cable-stayed bridge that was newly constructed in Fuzhou,China,this study is aimed at presenting an ambient vibration based proce-dure to establish a baselinefinite element model of the bridge.An initial full three-dimensionalfinite element model of the Qingzhou cable-stayed bridge isfirst con-ceived according to the original blue prints.Thefield ambient vibration tests were carried out just prior to opening the bridge.Two complementary modal para-meter identification techniques are implemented to obtain the basic dynamic characteristics of the bridge.They are rather simple peak picking(PP)method in frequency-domain and more advanced stochastic subspace identifi-cation(SSI)method in time-domain.The initialfinite element model is then verified with thefield test results in terms of frequencies and mode shapes.Some impor-tant issues in the modeling of such a complicated bridge have been clarified,such as the initial equilibrium config-uration due to dead load,geometrical nonlinearities, concrete slab,the shear connection of composite deck, and the longitudinal restraints of end expansion joints. The experimentally verifiedfinite element model can be used as a baseline for the dynamic health monitoring and succeeding dynamic response analysis of the bridge.2.Bridge descriptionThe Qingzhou cable-stayed bridge,as shown in Fig. 1,is one of the bridges on Luo-Chang Highway over the Ming River in Fuzhou,Fujian Province,China. The bridge has a composite-deck system consisting of five spans with an overall length of1186.34m (41.13m+250m+605m+250m+40.21m).Its605m main span is currently the longest span length among the completed composite-deck cable-stayed bridges, and ranks thefifth among the all types completed cable-stayed bridges all over the world.The bridge was completed in the year of2000,but it was officiallyW.-X.Ren,X.-L.Peng/Computers and Structures83(2005)536–550537opened to the traffic in the year of2002due to the con-struction delay of approach spans.Fig.2shows the sche-matic plan,elevation and deck cross-section views of the Qingzhou cable-stayed bridge.The bridge,having six lanes,carries two roadways with29m wide.The main structural features of the bridge are briefly described as follows.The composite-deck system of the bridge has an open-section consisting of two main I-type steel girders, steelfloor beams and25cm thickness concrete slab.The slender steel girder is2.45m high and its maximum plate thickness reaches80mm.The ratio of girder height to span length is about1/202.One steel stringer is designed in the middle of the cross-section.There are in total257 steelfloor beams with a spacing of4.5m.The precast concrete slab is connected to the steel girders andfloor beams by shear studs.The two diamond-shaped towers are of reinforced concrete.The height of the towers is175.5m with 145.5m above the bridge deck.The clear navigation is 43m.The towers are erected on a group of concrete-filled steel tube piles.The length of longest pile is71.6m.The cable arrangement is of fan type in both planes. There are in total21·8=168stay cables.The longest cable is over312m.The cables are composed of a num-ber of strands varied from27to85per cable in eight groups.One strand includes7high strength wires with the diameter of5mm(7B5high strength wires).3.Field ambient vibration testsOn November18–21,2002,just prior to officially opening the bridge,ambient vibration tests on the deck of the Qingzhou cable-stayed bridge were carried out. The equipment used for the tests included accelerome-ters,signal cables,and a32-channel data acquisition sys-tem with signal amplifier and conditioner.Accelerometers Fig.1.Qingzhou cable-stayedbridge.convert the ambient vibration responses into electrical signals.Cables are used to transmit these signals from sensors to the signal conditioner.The signal conditioner unit is used to improve the quality of the signals by removing undesired frequency content (filtering)and amplifying the signal.The amplified and filtered analog signals are converted to digital data using an analog to digital (A/D)converter.The signals converted to digital form are stored on the hard disk of the data acquisition computer.To identify acceptable three-dimensional mode shapes of the bridge,a quite dense measurement location on the bridge deck in the vertical,lateral and longitudi-nal directions was proposed.Measurement stations are chosen at each anchor position on the deck.As a result,there are in total 180measurement stations on the bridge deck,including several measurement stations at Span 1and Span 5.Measurement station arrangement on the bridge deck is shown in Fig.3where U refers to up-stream and D stands for downstream.Accelerometers were directly placed on the pavement due to limited ac-cess to the actual floor beams.Fig.4shows the accelero-meters mounted on the bridge deck in the vertical and horizontal directions.Fifteen low frequency force-balance accelerometers were used in the tests,of which 12accelerometers were moveable,while 3accelerometers were fixed as refer-ences.Reference locations,referred as the base stations,are selected according to the mode shapes from the pre-liminary finite element model.They were located at the center of side span (D15),the deck at Pier 2(U24)and the center of main span (U46).Fifteen test setups were proposed to cover all planned measurement locations of the bridge.Each setup yields a total of 15sets of data,12sets from the moveable stations and 3sets from the base stations.Once the data was collected in one setup,the moveable accelerometers were shifted to the next sta-tions while the base stations remained stationary.Mea-surements in the vertical,transverse and longitudinal directions were carried out separately in the same stations.During the all setups,the sampling frequency on site was 80Hz.The ambient vibration measurements weresimultaneously recorded for 20min at all channels.Typical tri-axial acceleration time history recordsatFig.4.Accelerometers mounted on deck:(a)vertical accelero-meters and (b)transverse accelerometers.W.-X.Ren,X.-L.Peng /Computers and Structures 83(2005)536–550539the station D46(main span center)are as shown in Fig.5.It is noted that tri-axial time series are not measuredsimultaneously.An inspection of the time history mea-Ambient vibration tests are not appropriate for fre-quency response function or impulse response functioncalculations because the input excitations are not mea-sured.Two complementary modal parameter identifica-tion techniques are implemented here.They are rathersimple peak picking(PP)method in the frequency-domain,and the more advanced stochastic subspaceidentification(SSI)method in the time-domain.Thedata processing and modal parameter identification werecarried out by using MACEC[20].The peak picking method is primarily based on thefact that the frequency response function goes throughan extreme around the natural frequencies.In the con-text of ambient vibration measurements,the frequencyresponse function is replaced by the auto spectra ofthe output-only data.To include the measurement chan-nels of all setups,the average normalized power spectraldensities(ANPSDs)are used.In such a way,the identi-fied natural frequencies are simply obtained from theobservation of the peaks on the graphs of ANPSDs.The ANPSDs of vertical and lateral acceleration mea-surements of all channels of the bridge deck are shown in Fig.6where the peaks can be clearly seen and then the frequencies can be picked up.The stochastic subspace identification technique is a time-domain method that directly works with time data, without the need to convert them to correlations or spec-tra.The stochastic subspace identification algorithm identifies the state space matrices based on the measure-ments by using robust numerical techniques.Once the mathematical description of the structure(the state space model)is found,it is straightforward to determine the modal parameters.The theoretical background is gi-ven in Van Overschee and De Moor[21],as well as Peet-ers[22].One of the advantages of the method is that the stabilization diagram can be constructed in an effective way by identifying a whole set of models at different or-der.The stabilization diagrams aid the engineer in select-ing the correct modes,whereas picking the peak is a subjective task.The benchmark studies of both methods have been carried out by Ren and Zong[23].The identified most significant frequencies of the Qingzhou cable-stayed bridge are summarized in Table 1.It can be seen that the identified frequencies agree well between the peak picking and stochastic subspace iden-tification methods.Most of the important frequencies of the bridge deck are below1.0Hz with the lowest fre-quency0.23Hz that is a symmetric deck bending in ver-tical direction.Vibration mode shapes of the bridge deck have been extracted by stochastic subspace identification.Fig.7 shows the identified most dominant mode shapes in ver-tical bending,transverse bending and torsion.The cou-pled3-D mode shapes can not obtained since vertical, transverse and longitudinal data are measured sepa-rately.It is demonstrated that the ambient vibration re-sponse measurements are sufficient to identify the most significant modes of such a large span cable-stayed bridge,despite the rather low level of ambient vibration signal captured,the low range(0–1.0Hz)of natural fre-quencies of interest,and the relatively dense modes of vibration in that range.A very good quality of the sym-metric vertical bending mode shapes as high as the9th mode(the5th symmetric vertical bending mode)has been extracted from ambient vibration measurements. However,the quality of the anti-symmetric vertical bending mode shapes is not so good.4.Finite element modeling of the bridge4.1.Simplified three-dimensionalfinite element modelsof cable-stayed bridgesContemporary cable-stayed bridges are complex,effi-cient and aesthetically pleasing structures which are appearing in various exotic forms.They involve a vari-ety of decks,towers and stay cables that are connected together in different ways.To reduce the degrees of free-dom and simplify the dynamic analysis,several simpli-fied three-dimensionalfinite element models of cable-stayed bridges were developed using elastic beam elements to model the towers and deck,and truss ele-ments to model the cables.The single-girder(spine)model is probably the earli-est three-dimensionalfinite element model of cable-stayed bridges in structural dynamics.The bridge deck was modeled using a single central spine with offset rigid links to accommodate cable anchor points.The deck stiffness was assigned to the spine,and mass(transla-tional and rotational)was assigned to the spine nodes. This simplified model neglects thefloor beam stiffness and girder warping,so it is suitable for a box section gir-der with relatively large pure torsional stiffness but small warping stiffness.To take the warping stiffness of the bridge deck into account in the single-girder beam element model,Wilson and Gravelle[5]presented a P-type model where theTable1Identified and calculated natural frequenciesNature of modes of vibration Peak-picking identification Stochastic subspace identification Finite element calculation1st vertical bending0.2270.2260.2222nd vertical bending0.2710.2720.2661st transverse bending0.2620.2630.2673rd vertical bending0.4440.4460.4154th vertical bending0.4820.4800.4545th vertical bending0.5060.5050.4781st torsion0.5550.5560.5517th vertical bending0.6090.6530.5712nd torsion0.6530.6100.6223rd torsion0.7010.7260.7122nd transverse bending0.7120.7280.7481st longitudinal 1.925 1.925 1.920W.-X.Ren,X.-L.Peng/Computers and Structures83(2005)536–550541deck stiffness and mass were separately treated.Due to the distribution of lumped mass on both sides,the rota-tion effect of deck mass can be automatically included.This model may produce coupling between torsional and lateral motions of the deck using an equivalent pure torsionalstiffness.Fig.7.Identified typical mode shapes below 1.0Hz.542W.-X.Ren,X.-L.Peng /Computers and Structures 83(2005)536–550For cable-stayed bridges with double cable planes and open-section deck systems,the double-girder model seems more natural.The double-girder beam element model consists of two girders located in each cable plane coupled tofloor beams.This model may include part of torsional stiffness through the opposite vertical bending of the two girders.Nazmy and Abdel-Ghaffar[3,4]suc-cessfully applied the model to the three-dimensional nonlinear earthquake-response analysis of long-span cable-stayed bridge.The warping stiffness of the open-section decks is one of the most difficult parameters to estimate in developing a model of cable-stayed bridges.Zhu et al.[6]presented a triple-girder beam element model consisting of one central girder and two side girders to include the warp-ing stiffness properly.If deck stiffness and mass are cor-rectly equalized and distributed to three girders,the warping stiffness can be effectively considered.The model was verified through a comparison with the mea-sured dynamic results of the Nanpu cable-stayed bridge.The modeling of a deck system is relatively ambigu-ous by using simplified beam element models.The adequacy of the simplified models is particularly ques-tionable when representing the bridge deck system in the lateral and torsional vibration.The lateral vibration modes may be distorted to some extent if the deck stiffness equivalence is treated improperly.A dynamic study on the composite-deck system of an arch bridge has shown that thefirst lateral frequency of the triple-girder model is twice that of the double-girder model [24].Relatively large differences of torsional frequencies were also found between two models.Ren et al.[25] verified the stiffness contribution of the concrete slab throughfinite element analysis andfield ambient vibra-tion tests on a steel arch bridge with a composite-deck system.The concrete slab may have less effect on the vertical bending stiffness,but may be a large contribu-tion to the lateral and torsional stiffness of the bridge deck.To represent the bridge dynamic behavior well, instead of simplified beam element models,a full three-dimensionalfinite element model is required with several types of elements such as beam elements,truss elements,shell elements,solid elements and link ele-ments representing different components of cable-stayed bridges.Creating a good three-dimensional dynamicfinite ele-ment model for cable-stayed bridges is not an easy task. Many different modeling strategies(i.e.,which element types,how many degrees of freedom,etc.)are possible. The choice of strategy depends on the skill and experi-ence of the analyst and on the intended application of the model.The baselinefinite element model for struc-tural dynamics needs an accurate representation of the bridge dynamic behavior.However,extremely large computational effort is required depending on the num-ber of degrees of freedom in the model.There is no un-ique way to conclude that the model developed is the best.4.2.Full three-dimensionalfinite element modeling of the Qingzhou cable-stayed bridgeAimed at establishing a baselinefinite element model for the long-term health monitoring of the Qingzhou cable-stayed bridge,a full three-dimensionalfinite model is conceived in ANSYS[26]because of the programÕs significant capability to account for the initial cable ten-sion and pre-stressed modal analysis capability.The geometry and member details of the model are based on the design information and design blue prints of the bridge.The main structural members are composed of stay cables,girders,floor beams,concrete slab and towers,all of which are discreterized by differentfinite element types.Modeling of the stay cables is possible in ANSYS by employing the3-D tension-only truss elements (LINK10),and utilizing its stress-stiffening capability. With this element,the stiffness is removed if the element goes into compression,thus simulating a slack cable.No bending stiffness is included,whereas the pre-tensions of the cables can be incorporated by the initial strains of the element.The stress-stiffening capability is needed for analysis of structures with a low or nonexisting bend-ing stiffness as is the case with cables.The cable sagging effect can be considered with the stress-stiffening capabil-ity.The element is nonlinear and requires an iterative solution.Each stay cable is modeled by one element, which results in168tension-only truss elements in the model.Two steel girders and one central stringer are mod-eled as the3-D elastic beam elements(BEAM4),since they are the structural members possibly subjected to tension,compression,bending and torsion.There are in total968elements of this type.The side spans include T-type concrete beams that are also discreterized by the BEAM4element that results499elements.Thefloor beams are of variable sections and thus they are modeled by the BEAM44elements.Five hun-dred andfifty-four elements of this type are used in the current model.Towers consist of both equivalent and variable sections so they are discreterized by both BEAM4and BEAM44elements with a total number of140.All piers and platforms are modeled by the solid elements(SOLID45),of which there are193.The con-crete slab is divided into508shell elements(SHELL63). In addition,210concentrated mass elements(MASS21) are used to include the mass of equilibrium blocks,par-apet and anchors that are nonstructural members.The modeling of bridge boundary conditions is an important issue in the dynamic analysis.Two types of bridge bearings are used in the Qingzhou cable-stayed bridge.Fixed bearings are applied to Pier2,whileW.-X.Ren,X.-L.Peng/Computers and Structures83(2005)536–550543expansion bearings are used for the rest piers.In the cur-rent model,bridge bearings are modeled by a set of rigid link elements connecting the superstructure and piers. To simulate the actual behavior,thefixed and expansion bearings are simulated by coupling the corresponding translational and rotational degrees of freedom at both end nodes of the link elements.In addition,there are expansion joints at Pier0and Pier 5.Longitudinal springs(COMBINE14)are then applied to account for the restraining action in the longitudinal direction.One hundred and sixty-eight stay cables are divided into eight groups.Their material and geometric proper-ties are listed in Table2.The basic material properties of other structural members are summarized in Table3. The full three-dimensionalfinite element model of the Qingzhou cable-stayed bridge is shown in Fig.8.The complete model consists of1840nodes and3238ele-ments resulting in9193active degrees of freedom (DOFs).The model represents the bridge in its current as-built configuration and structural properties.5.Some important aspects in modeling of the Qingzhou cable-stayed bridge5.1.Initial equilibrium configurationOne of the important features of a large span cable-stayed bridge is that the dead load(self weight)is often dominant.The pre-tensions in the stay cables control the internal force distribution in the deck and towers as well as the bridge alignment.The initial equilibrium configu-ration of cable-stayed bridges is therefore the equilib-rium position due to dead load and tension forces in the stay cables.The initial equilibrium configuration is important in cable-stayed bridges since it is a starting position to perform the succeeding analysis.In this newly constructed cable-stayed bridge,the ini-tial deformed equilibrium configuration of thefinite ele-ment model should be identical to the completed initial geometry alignment of the bridge deck.This can be real-ized by manipulating the initial tension force in each stay cable that is specified as an input quantity in the cable elements.The design cable tensions arefirst ap-plied to each stay cable and the static analysis under dead load is carried out to compare the calculated deck alignment with the measured deck alignment.The cable tensions are then adjusted until the best match is achieved.The comparisons offinal calculated upstream and downstream deck alignments with the measured alignments are shown in Fig.9.The adjustment of each cable tension is within9%compared with the designTable2Properties of stay cablesCable no.Number of strands Area(cm2)Length density(kg/m)E(MPa) C1–C4,S1–S427–B1537.8032.79C5–C6,S5–S634–B1547.5941.39C7–C9,S7–S837–B1551.7944.94C10–C12,S9–S1043–B1560.1952.22 1.95·105 C13–C14,S11–S1348–B1567.1958.30C15–C1855–B1576.9966.80C19–C2073–B15102.1988.66C21,S20–S2185–B15118.93103.23Table3Material properties of structural membersMaterials E(MPa)Density(kg/cm3)Structural membersSteel 2.10·1057850Girders,floor beams,stringer Concrete C30 3.00·1042550Platform of piersConcrete C40 3.25·1042550PiersConcrete C50 3.45·1042550Towers,T-beamsConcrete C60 3.60·1042550ConcreteslabFig.8.Full three-dimensionalfinite element model of thebridge.544W.-X.Ren,X.-L.Peng/Computers and Structures83(2005)536–550。
鲨鱼表皮的仿生原理对人类的作用英语作文全文共3篇示例,供读者参考篇1The biomimetic principles of shark skin and their implications for humansIntroductionSharks are one of the most fascinating creatures in the ocean, known for their sleek bodies and powerful swimming abilities. One of the key features that contributes to their efficiency in the water is their unique skin. Shark skin is covered with tiny scales called dermal denticles, which have a structure that is now being studied and replicated for various human applications. This process is known as biomimicry, where engineers and scientists draw inspiration from nature to design innovative solutions to human problems.The structure of shark skinDermal denticles are small, tooth-like structures that cover the skin of sharks. These denticles are aligned in a specific pattern that reduces drag and turbulence as the shark swims through the water. The scales have a shape that resembles tinytooth-like structures, with ridges that run parallel to the flow of water and tiny riblets that break up the boundary layer, reducing friction. This unique design allows sharks to move efficiently through the water, enabling them to reach high speeds and maneuver quickly.Applications for human technologyThe biomimetic properties of shark skin have inspired researchers to develop new technologies and materials for human use. One of the most significant applications is in the field of aerodynamics, where the design of aircraft and vehicles is being improved to reduce drag and increase efficiency. By mimicking the structure of shark skin, engineers have been able to design surfaces that are more hydrodynamic and produce less noise, leading to improved performance and fuel efficiency.Another area where shark skin biomimicry is being applied is in the development of antimicrobial surfaces. The unique pattern of shark scales has been found to inhibit the growth of bacteria and pathogens, making it an ideal inspiration for creating surfaces that are resistant to microbial contamination. These antimicrobial materials have the potential to be used in healthcare settings, food processing facilities, and other critical environments where cleanliness is essential.Furthermore, the properties of shark skin are being harnessed for the development of new materials that can be used in underwater equipment and marine structures. By replicating the design of shark scales, researchers have been able to create coatings that reduce biofouling and corrosion, improving the durability and performance of underwater devices. These materials have the potential to revolutionize the marine industry by providing solutions that are more sustainable and environmentally friendly.Implications for sustainability and conservationIn addition to the technological advancements that have resulted from studying shark skin, there are also important implications for sustainability and conservation. By understanding and appreciating the intricate design of shark skin, we can gain a greater appreciation for the importance of preserving these magnificent creatures and their habitats. As sharks are facing increasing threats from overfishing and habitat destruction, it is crucial to recognize the value of their unique adaptations and the role they play in maintaining the balance of marine ecosystems.Furthermore, the development of biomimetic technologies that are inspired by shark skin can contribute to efforts toprotect the environment and reduce our impact on the planet. By designing materials and products that are more efficient, durable, and environmentally friendly, we can create a more sustainable future for ourselves and future generations. The study of shark skin serves as a powerful reminder of the incredible diversity and ingenuity of nature, and the importance of preserving and learning from the natural world.ConclusionThe biomimetic principles of shark skin have opened up a world of possibilities for human innovation and sustainability. By studying and replicating the unique structure of shark scales, researchers have developed new technologies and materials that have the potential to revolutionize industries and improve the quality of human life. Furthermore, the study of shark skin serves as a poignant reminder of the interconnectedness of all living things and the importance of protecting and conserving the natural world. As we continue to explore and learn from the wonders of nature, we can unlock new solutions to the challenges we face and create a more harmonious relationship with the planet.篇2Title: The Biomimetic Principle of Shark Skin and its Impact on HumanityIntroductionIn recent years, biomimicry, the practice of imitating natural biological processes in technology and design, has gained popularity as a sustainable and innovative solution to various challenges faced by humanity. One of the most fascinating examples of biomimicry is the replication of shark skin in various products and applications. The unique properties of shark skin have inspired scientists and engineers to develop materials and technologies that offer numerous benefits to human society. This essay will explore the biomimetic principle of shark skin and its impact on humanity.The Biomimetic Principle of Shark SkinShark skin is covered with millions of tiny, tooth-like scales called dermal denticles. These scales have a riblet structure that reduces drag and turbulence in water, allowing sharks to swim faster and more efficiently. This unique surface texture has inspired the development of biomimetic materials that can be used in a wide range of applications, from swimwear and sports equipment to airplanes and ships.Impact on HumanityThe biomimetic principle of shark skin has had a significant impact on humanity in various fields:1. Sports and Recreation: The biomimetic design of shark skin has been incorporated into swimsuits, wetsuits, and sports equipment to enhance performance. Athletes wearing shark skin-inspired gear have reported improved speed, agility, and endurance, leading to better results in competitions.2. Transportation: The riblet structure of shark skin has been used to design more aerodynamic vehicles, such as airplanes, trains, and cars. By reducing drag and turbulence, these vehicles can achieve higher speeds and greater fuel efficiency, contributing to a more sustainable transportation system.3. Medical Technology: The anti-bacterial properties of shark skin have inspired the development of biomimetic materials for medical devices, such as implants and wound dressings. These materials can prevent infections and promote faster healing, improving the effectiveness of medical treatments.4. Environmental Conservation: The biomimetic design of shark skin has raised awareness about the importance of preserving marine biodiversity. By studying and mimicking thenatural adaptations of sharks, scientists and engineers can develop sustainable solutions to protect and conserve ocean ecosystems.ConclusionThe biomimetic principle of shark skin has revolutionized various industries and has the potential to transform human society in the future. By harnessing the unique properties of shark skin, scientists and engineers can develop innovative materials and technologies that offer sustainable solutions to complex challenges. The impact of biomimicry extends beyond practical applications and serves as a reminder of the wonders of nature and the importance of preserving biodiversity for future generations.篇3The Bio-Inspired Principles of Shark Skin and Their Impact on HumansIntroductionSharks have roamed the oceans for over 400 million years, making them one of the Earth's oldest and most successful species. One of the key factors contributing to their longevity and efficiency as predators is their unique skin structure. Sharkskin is covered in tiny tooth-like scales called dermal denticles, which have inspired scientists to develop innovative technologies with applications in various fields. This article will explore the bio-inspired principles of shark skin and their potential impact on humans.Bio-Inspired DesignThe surface of shark skin is covered in thousands of tiny dermal denticles, which are shaped like miniature teeth. These denticles have a unique structure with riblets that run parallel to the shark's body, reducing drag and turbulence as water flows over the skin. This design helps sharks move through the water with minimal resistance, making them swift and efficient predators.Scientists have replicated the structure of shark skin to develop biomimetic materials that have a wide range of applications. For example, the riblet design has been incorporated into the design of swimsuits and wetsuits, reducing drag and improving the performance of competitive swimmers. In addition, shark-inspired coatings have been developed for ships and submarines to reduce fuel consumption and increase speed by up to 10%. These innovations have the potential torevolutionize industries such as sports, transportation, and defense.Medical ApplicationsThe unique properties of shark skin have also inspired medical researchers to develop innovative solutions for healthcare. The antibacterial properties of shark skin have been studied and replicated to create antibacterial coatings for medical devices and implants, reducing the risk of infections in patients. In addition, the riblet structure of shark skin has been used to design bandages and wound dressings that promote faster healing by reducing friction and preventing bacterial growth.Furthermore, researchers are exploring the potential of shark skin-derived materials in regenerative medicine. The collagen fibers in shark skin have been found to have high tensile strength and durability, making them ideal for tissue engineering and wound healing applications. By harnessing the regenerative properties of shark skin, scientists aim to develop advanced therapies for tissue repair and regeneration.Environmental ImpactIn addition to their applications in technology and medicine, the bio-inspired principles of shark skin have the potential to address environmental challenges such as pollution and climate change. The development of shark-inspired materials for water filtration and desalination could provide sustainable solutions for clean water access in developing countries. Furthermore, the use of shark-inspired coatings in renewable energy technologies such as wind turbines and solar panels could increase efficiency and reduce environmental impact.ConclusionThe bio-inspired principles of shark skin have the potential to revolutionize various industries and address pressing global challenges. By understanding and replicating the unique structure and properties of shark skin, scientists are developing innovative technologies with applications in sports, healthcare, and environmental sustainability. As we continue to explore the capabilities of shark-inspired materials, we may unlock new opportunities for improving human health, protecting the environment, and advancing technology.。
Rigid Body DynamicsProfessor Sanjay SarmaNovember 16, 20071.0 Where are we in the course?Thus far we have completed Kinematics and Kinetics of single particles, systems of particles and rigid bodies respectively. We are now well into the Lagrange portion of the class.SystemParticleSystem of particles Rigid Bodies Lagrangian formulation Oscillations Kinematics Kinetics & ConstitutiveNext2.0 Generalized CoordinatesThe generalized coordinates of a mechanical system are the minimal group of parameters which can completely and unambiguously define the configuration of that system. Some generalized coordinates are more “natural” than others, but there might be many ways to define them for any one system. The number of generalized coordinates equals the number of degrees of freedom of the system as long as the system is holonomic. We only study holonomic systems in this class.Consider a system consisting of N rigid bodies in 2D space. Each rigid body has 3 degrees of freedom: two translational and one rotational. The N-body system has 3n degrees of freedom. Now let’s say that there are k kinematic constraints which can be expressed as algebraic equations. Then the system has d =3N k degrees of freedom.–The term “holonomic” refers to the fact that the kinematic constraints must be expressible as algebraic equalities. Some kinematic constraints can only be expressed as inequalities or differential equations. Such systems are called non-holonomic constraints. We will not consider non-holonomic systems in this class— if you are interested in such systems, you can talk to me about them outside class.3.0 Why Lagrange?There are several reasons why the Lagrange Approach is important.1. The Lagrange Approach automatically yields as many equations as there are degrees offreedom. It has the convenience of energy methods, but whereas energy conservationonly yields just one equation, which isn’t enough for a multi-degree-of-freedom system, Lagrange yields as many equations as you need.2. The Lagrange equations naturally use the generalized coordinates of the system. Bycontrast, Newton’s Equations are essentially Cartesian. You end up having to converteverything into Cartesian components of acceleration and Cartesian components offorces to use Newton’s Equation. Lagrange bypasses that conversion.3. The Lagrange approach naturally eliminates non-contributing forces. You could do thesame with the direct (Newtonian) approach, but your ability to minimize the number ofvariables depends very much on your skill; Lagrange takes care of it for you automatically because the generalized forces only include force components in directions ofadmissible motion .4.0 The Lagrange EquationsFor a d -dof (degree-of-freedom) system with generalized coordinates q j ’s, it is possibleto formulate the Lagrangian L = T – V where T is the kinetic energy and V is the potential energy . The Lagrangian is a function of generalized coordinates q j ’s and generalized· velocities q j ’s:·· L q 1,, q 1,…q · ) .1 (EQ 1)L = (…q j …q d …q j d where d is the number of degrees of freedom.The Lagrange Equations are then:d d t ⎛⎝∂∂ L q · j ⎞⎠ – ∂∂L q j = Q j , (EQ 2)where Q j ’s are the external generalized forces. Since j goes from 1 to d , Lagrange gives usd equations of motion.But what are generalized forces? We derived them in class. Read on.4.1 Generalized ForcesThe generalized force Q j is defined below:1. There are some situations in which the Lagrangian is explicitly a function of time. Such systems arecalled rheonomic systems. We will not explore the implications in this course.q xy δqΔyΔxFIGURE 1. A bead on a wireQ j = F i i = 1 N ∑ • ∂q j ∂r i ⎝ ⎠ ⎜ ⎟ ⎛ ⎞ (EQ 3)where F i is the force at point i and r i is the position vector of point i . The index j corresponds to generalized coordinates.4.2 The IntuitionSo why does the Lagrange formulation work? The insight is simple. The Lagrange formulation only considers admissible motions .4.2.1 The Problem with the Newtonian ApproachConsider a bead sliding without friction on a curved wire as shown in Figure 2. Clearly thebead can only move along the wire, which can be approximated locally as a direction tangential to the wire. Now, the Cartesian coordinates of the bead would be x and y . However,these coordinates are redundant. We can only eliminate the redundancy by introducing ageometric constrain between x and y of the form Constraint x y (, ) = 0 .1 For example, ifthe wire is in the form of a circle of radius R , the constraint will be x 2+ y 2– R 2= 0. Nocombination of Δx and Δy is legal if it does not satisfy x 2+ y 2– R 2= 0.In the direct, or Newtonian approach, we waste a lot of time considering x and y motionsas if the bead could get to any x and y (which it can’t), postulating reaction forces (whichare actually irrelevant) and then solving for these reaction forces and motions such that theΔx and Δy satisfy the kinematic constraint (which is a waste of time). The problem, as 1. We will assume that this is an algebraic. If it is an inequality constraint or an unintegrable differentialequation, we need more machinery which we will not cover in this course.12Let’s say you tryto move in thisdirection.5 A reaction forcekeeps the bead onthe wire.3 This reaction force is irrelevant because it adapts to counter any applied force, and it doesn’t do work.4 So why even consider impossible motions and the forces we need to make them vanish? They don’t impact the dynamics of the system.So if we only consider motions which are in admissible directions and the forces in thesedirections, we can solve the kinetics of the problem. Hello Lagrange!FIGURE 2. Admissible motions and the non-contributing forces that enforce themshown in Figure 2, is that we do everything explicitly and in the process, we end up solving for a number of extra variables like reaction forces and inadmissible motions whichend up being irrelevant to the actual dynamics of the system. Essentially, pushing at animmovable object causes to motion.4.2.2 Admissible MotionsHere’s the rub. The use of a good set of generalized coordinates eliminates this problembecause generalized coordinates implicitly capture admissible motions . For example, ifour wire is in the shape of a circular loop, an appropriate generalized coordinate is theangle of bead on the wire loop as shown in Figure 3 (a). If our wire were a cosine shape, itwould look like Figure 3 (b) (I will concentrate on the circle in these notes, and leave it toyou to work the math out for the sinusoid.) Now, consider the position vector r written as afunction of q for the circular loop:r q = (R cos q )+ (R sin q )a 2.() a 1 qq FIGURE 3. Different wire shapes and relevant generalized coordinatesa) A circular loopb) A sinusoidal wire r r a 1 a 2R A F q ∂ ∂r A (admissibledirection ofmotion)q ∂ ∂r A FA∂rNow consider the expression . (We were sloppy about specifying the frame for the derivative in the past, and we will omit it in the future under the assumption that when not stated, the frame of reference for a derivative is the inertial frame A.) Let’s compute this expression:∂r=– (R sin q)a1+ (R cos q)a2.Guess what, this vector is tangential to the circle and instantaneously captures the admissible motion of the bead. A small variation of q, δq, results in a δr given by:δr = ∂rδq .(EQ4)δr is an admissible motion for the bead. It captures the kinematic constraint. In general, in a d-degree-of-freedom system with generalized coordinates q1,…,q d , the admissible motions at a point i with position vector r i are given by:d δr i = ∑∂r ijδq j .(EQ5)j =1Note that the symbol δ in front of a variable emphasizes that the motion is an implicitly admissible motion. The d-dimensional version is actually a d-dimensional tangent space just like in a 1-dof case.4.2.3 f = m a Written as Components in Admissible DirectionsIf you applied a force F on the bead shown in Figure 1, the only component which is relevant, assuming the wire is rigid, is the component of the force along the admissible direction. For the bead, this is given by ∂∂rq. So the only force component we need to worryabout is:∂rF •∂q .(EQ6)All other forces are perpendicular to the motion and don’t do any work! Of course, ∂∂r qisn’t a unit vector, and its dimensions are those of a length, but don’t worry about that for a moment. What we have just derived is the generalized force for a 1-dof system.Newton’s Law says F = m a . We have just accounted for the LHS along the admissibledirection. Similarly, the only acceleration component we need to worry about is the one inan admissible direction, and the RHS of Newton’s Equation of motion can be written as:∂r ··m r• (EQ 7)∂q when we recognize that a = r··. So taking the components of Newton’s Laws in the admissible direction only, we get:F • ∂r = m r ··• ∂r . (EQ 8)or, looking at work, we get:∂r ∂r F •δq = m r ··•δq . (EQ 9)Look familiar? This is how we started our derivation of Lagrange’s Equations. This leadsto the 1-dof Lagrangian Equation. The LHS is Q , the generalized force. Essentially, the RHS of Equation 8 reduces to:d ⎛⎞∂L ∂L Q = ⎝⎠– . (EQ 10)dt · Look up the derivation from class to see why. You can extend this reasoning to multi-dofsystems and get the general Lagrangian Equation:d ∂L ∂L ⎛⎞– = . (EQ 11)·dt ⎝∂q j ⎠∂q j Q j 4.2.4 Generalized Forces AgainSo the key matter regarding generalized forces is this:• Forces of constraint which do not do work can be ignored because they will alwaysbe perpendicular to admissible directions. Examples include the internal forces in arigid body, the forces of reaction in friction-less sliding, and so on.• Forces which derive from a potential function like gravity or a spring can be considered in potential energy, V . They too can be ignored when computing generalizedforces.• Internal forces in rigid bodies do not contribute.• Forces in pure rolling don’t contribute.• Forces which are none of the above need to be called out and used in Formula 3. Wewill call such forces contributing forces. Examples include dissipative forces fromdashpots, externally applied forces and so on. You can’t go wrong including a forcein this category instead of one of those above because they will vanish or beaccounted for appropriately here.5.0 Using Lagrange’s EquationsThe steps in computing the equations of motion using Lagrange’s method are below.Start with the LHS of Equation 11:1. Identify the generalized coordinates. Make sure that you have just as many as thereare degrees-of-freedom.2. Compute the kinetic energy T as a function of q j ‘s and q · j‘s. 3. Compute the potential energy V as a function of q j ‘s and q · j‘s. Clearly mark out the forces which you will call out as potential and forces which you will call out asexternal4. Compute L = T – V , which will obviously be a function of q j ‘s and q · j‘s. 5. Compute d ⎛ ⎞ ∂L and ∂L and you have the LHS for each j .dt ⎝· j ⎠jNow the RHS of Equation 11:1. Identify all contributing forces.2. Number them as i =12 …n . Call the forces F 1, F 2,...F n .,, 3. Identify the precise points where the forces are applied on the system, and identifyr 2 r j must be athe position vectors r 1,,…,r n respectively for all these points. Each function of q j ‘s.n⎛⎞ 4. For each j , compute the generalized force using Equation 3: Q j =∑F i •⎜∂∂r q i j ⎟. ⎝⎠i =1 Now equate the LHS to RHS for each j . -------------------------------------------------Done--------------------------------------------------。
Earthing sticksFor installation and removal of earthing and short-circuiting devices inhigh-voltage installations Designed according to VDE 0683-100 (IEC 61230) Material: fibreglass reinforced epoxy resin tube Types: bayonet or hexagonal fitting Application for indoorinstallationsProduct features1) Dimensions apply to earthing sticks with bayonet fitting. Earthing sticks with hexagonal fitting are 12 mm longer.Indoor application earthing stickOrder no.b Bayonet fitting Hexagon fitting 1,11771766-0101-00166-0201-0011,51791766-0101-00266-0201-0022,0171.21766-0101-00366-0201-003baThe insulating element of the earthing stick must be of adequate dimension to avoid inadmissible high leakage currents. The minimum length of the insulating element is 500 mm.Hot sticksManual operation of live partsDesigned according to DIN VDE 0681-1 Material: fibreglass reinforced epoxy resin tube Types: bayonet or hexagonal fitting Application for indooror outdoor installationProduct featuresNominal voltage range [kV]Dimensions [mm]Order no.a bc Bayonet fitting 1 — 361,7071,20010765-0102-001Outdoor application hot stickbac With hook for applications in dry weather conditionsThe hook serves to mount and dismount elbow connectors and for overhead faulted circuit indicator installations and removals.Hot stick with hookNominal voltage range [kV]Dimensions [mm]Order no.a b c 1 — 241,200500 31065-0301-001b ac bac 1) Dimensions apply to hot sticks with bayonet fitting. Hot sticks with hexagonal fitting are 12 mm longer.Indoor application hot stickDimensions [mm]Order no.a 1)b c1)Bayonet fitting Hexagon fitting 1 — 241,11750021765-0101-00165-0201-001Operating rodsUsed to switch on and off switches with ring eyesSwitch hook with bayonet fittingSuitable for all hot sticks (bayonet fitting according to DIN 48087)Product features1) Dimensions only for two-part operating rods.Indoor application operating rodabcdDimensions [mm]Order no.a b c d 1)One-part Two-part 1 — 241,12050521560065-0401-00165-0403-001Nominal voltage range [kV]Dimensions [mm]Order no.a bc 1 — 241,5201,00012065-0402-001Outdoor application operating rodabc Designed according to VDE 0681-2 (DIN 57681-2) Material: fibreglass reinforced epoxy resin tube One-part and two-part pluggable design Application for indooror outdoor installationFuse tongsFor gripping and replacing high-voltage HH fusesTotal length [mm]Order no.Tools for fusesMaterial: Special brassabcDimensions [mm]Clamping range [mm]Order no.a b c 1) 1 — 36 kV1,0105308550 — 9065-0502-002Fuse tong type KThe fuse tongs are guided over the fuses from the front, thus requiring little spaces to the side. They are ideally suit-ed for use in narrow installations. The clamps are fixed and released by turning the handle.According to DIN VDE 0681-3Product features1) In closed position.Fuse testing devicesFuse testing device and extension The mechanical HPS fuse testing device is designed to control the trip function of load break switches.The testing fuse consists of a cylindrical fuse body similar to that of HH fuses and is fitted with a mechanical release device, timer and striker pin.After winding up the timer the striker pin is reset and the testing device is inserted into the fuse cartridge of the switch to be checked.After about 150 s ±20 % the test fuse is operated whereup-on the striker fires out. The size of the fuse corresponds to that of HH fuses with 6 kV nominal voltage. Extension piec-es are available for the adaptation to other voltage levels.4 mm [N] 28.220 mm [N] 20.84 mm [N] 39.020 mm [N] 27.24 mm [N] 44.120 mm [N] 28.74 mm [N] 60.120 mm [N] 40.64 mm [N] 74.720 mm [N] 53.3Accessories Un [kV]Order no.ExtensionFusetestingdeviceExtension±273519233x34Ø61Ø45Ø8Wall holdersFor safety materialFor voltage detectors52-0105-00152-0105-002AccessoriesRed / white with nylon linksdioxide, with snow pipe andLED work lampIncl. wall-mounting charge sta-tion with charge status display, flashing and emergency lightSafety helmetWithout face shieldFor electricians, 1,000 Vaccording to VDE 0680-1 with certification stamp, length:Rubber insulating matting Up to 50 kV, max. 1 m wide, 4 mm thick, 10 m long。
专利名称:RIGID CABLE HARNESS WITH A CURABLESLEEVE AND METHOD FOR FORMING SUCHCABLE HARNESS发明人:Dibble, Brett,Oliver, Robert,Meier,Andreas,Böcker, Patrick申请号:EP18210816.7申请日:20181206公开号:EP3499664A1公开日:20190619专利内容由知识产权出版社提供专利附图:摘要:Provided are methods for forming a rigid cable harness. An example method includes providing a curable sleeve comprising a curable compound, an adhesive, and a backing; wherein the curable adhesive tape has a longitudinal direction. The method further includes placing a plurality of cables on the sleeve in the longitudinal direction and wrapping the curable sleeve around the placed plurality of cables to form a cable harness, wherein the wrapping comprises wrapping the plurality of cables with thecurable sleeve in the longitudinal direction. The method additionally includes positioning the cable harness into a desired shape and curing the curable compound of the cable harness to form the rigid cable harness, wherein the rigid cable harness has the desired shape.申请人:tesa SE地址:Hugo-Kirchberg-Strasse 1 22848 Norderstedt DE 国籍:DE更多信息请下载全文后查看。
8-1462039-3Axicom IM, Signal Relays, 250VAC Contact Voltage Rating, 220VDC Contact Voltage Rating, 140mW Signal Relay Coil Power Rating (DC)Relays, Contactors & Switches > Relays >Signal RelaysInsertion Loss (HF Parameter):-.03dB @ 100MHz, -.33dB @ 900MHzIsolation (HF Parameter):-18.8dB @ 900MHz, -37dB @ 100MHzSignal Relay Coil Power Rating (DC):140 mWContact Voltage Rating:220 VDCFeaturesProduct Type Features Relay Type IM Relay Product TypeRelayElectrical Characteristics Coil Power Rating Class 50 – 300 mW Actuating SystemDC Insulation Initial Dielectric Between Open Contacts 750 Vrms Contact Limiting Short-Time Current5 A Insulation Initial Dielectric Between Contacts and Coil 1500 Vrms Insulation Initial Dielectric Between Coil/Contact Class 1000 V – 1500 VAVoltage Standing Wave Ration (HF Parameter) 1.06 @ 100MHz, 1.49 @ 900Mhz Insulation Initial Dielectric Between Adjacent Contacts 750 Vrms Insulation Initial Resistance 1000000 MΩContact Limiting Making Current 5 A Coil Resistance178 ΩContact Limiting Continuous Current 5 A 8-1462039-3 ACTIVEAxicom TE Internal #:8-1462039-3Axicom IM, Signal Relays, 250VAC Contact Voltage Rating, 220VDC Contact Voltage Rating, 140mW Signal Relay Coil Power Rating (DC)View on >Axicom IM|Coil Type MonostableContact Limiting Breaking Current 5 AContact Switching Load (Min).1mA @ .0001VContact Voltage Rating220 VDCSignal Relay Coil Power Rating (DC)140 mWSignal Relay Coil Voltage Rating 5 VDCSignal Relay Contact Switching Voltage (Max)220 VDCSignal Relay Coil Magnetic System Monostable, DC, PolarizedSignal CharacteristicsIsolation (HF Parameter)-18.8dB @ 900MHz, -37dB @ 100MHz Insertion Loss (HF Parameter)-.03dB @ 100MHz, -.33dB @ 900MHz Body FeaturesInsulation Special Features2000V Initial Surge Withstand VoltageBetween Contacts & CoilWeight.75 g[.026 oz]Contact FeaturesContact Plating Material GoldContact Current Class0 – 5 AContact Special Features Bifurcated/Twin ContactsSignal Relay Terminal Type PCB-THTSignal Relay Contact Current Rating 5 ASignal Relay Contact Arrangement 2 Form C (2 CO)Contact Material AgNi+AuContact Number of Poles2Termination FeaturesTermination Type Through HoleMechanical AttachmentSignal Relay Mounting Type Printed Circuit BoardDimensionsWidth Class (Mechanical)0 – 6 mmWidth 6 mm[.222 in]Height 5.65 mmLength Class (Mechanical)0 – 10 mmLength10 mm[.393 in]Height Class (Mechanical)0 – 6 mmDimensions (L x W x H) (Approximate)10 x 6 x 5.65 mm[.393 x .236 x .222 in] Usage ConditionsEnvironmental Ambient Temperature (Max)85 °C[185 °F]Environmental Ambient Temperature Class70 – 85°CEnvironmental Category of Protection RTVOperating Temperature Range-40 – 85 °C, -40 – 85 °COperation/ApplicationPerformance Type High CurrentPackaging FeaturesPackaging Method TubeProduct ComplianceFor compliance documentation, visit the product page on >EU RoHS Directive 2011/65/EU CompliantEU ELV Directive 2000/53/EC CompliantChina RoHS 2 Directive MIIT Order No 32, 2016No Restricted Materials Above ThresholdEU REACH Regulation (EC) No. 1907/2006Current ECHA Candidate List: JUN 2020(209)Candidate List Declared Against: JUL 2019(201)Does not contain REACH SVHCHalogen Content Low Bromine/Chlorine - Br and Cl < 900ppm per homogenous material. Also BFR/CFR/PVC FreeSolder Process Capability Wave solder capable to 265°CProduct Compliance DisclaimerThis information is provided based on reasonable inquiry of our suppliers and represents our current actual knowledgebased on the information they provided. This information is subject to change. The part numbers that TE has identified asEU RoHS compliant have a maximum concentration of 0.1% by weight in homogenous materials for lead, hexavalentchromium, mercury, PBB, PBDE, DBP, BBP, DEHP, DIBP, and 0.01% for cadmium, or qualify for an exemption to theselimits as defined in the Annexes of Directive 2011/65/EU (RoHS2). Finished electrical and electronic equipment productswill be CE marked as required by Directive 2011/65/EU. Components may not be CE marked. 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Regarding the REACH Regulation, the information TE provideson SVHC in articles for this part number is based on the latest European Chemicals Agency (ECHA) ‘Guidance onrequirements for substances in articles’ posted at this URL: https://echa.europa.eu/guidance-documents/guidance-on-reachTE Model / Part #9-1614350-6RN 0603 12R4 0.1% 10PPM 1K RLTE Model / Part #1622807-5SIL 10PIN 9RES 10K 5%TE Model / Part #6-1879621-9H4P 6K8 1% 50PPMTE Model / Part #1-1879628-5H4P 510K 1% 100PPMTE Model / Part #1-2176306-3RP 1E 0.1W 1K54 0.1% 25PPM 5K RLTE Model / Part #4-2337939-8PCIE GEN4 CON,SMT,164POS,15u",MYLAR,HTTE Model / Part #3-2176315-0MELF SMA_A 27K 0.1% 15PPM 0204 0.4WTE Model / Part #2041215-10.5mm FPC ConnectorsSignal Relays(122)RJ45 Connectors(2) TE Model / Part #9-1462038-9IM03DGR=IM RELAY 140MW 5VTE Model / Part #CAT-AX41-IM11B IM STANDARD (2 FORM C, 2CO CONTACTS)Compatible PartsAlso in the Series Axicom IMCustomers Also BoughtTE Model / Part #413515-7JACK,DECOUPLER,RTANG,BNC PCBTE Model / Part #3-644461-707P MTA156 CONN ASSY 18AWG LFDocumentsProduct DrawingsIM03DTS=IM RELAY 140 MW 5 VEnglishDatasheets & Catalog PagesTransportation, Storage, Handling, Assembly and Testing of Axicom Through Hole Terminal (THT) RelaysEnglishIM Relay DatasheetEnglishIndustrial Relays Quick Reference GuideEnglish。
科学家研发出可贴在皮肤上的自供电心脏监测器
郭琳
【期刊名称】《海南医学》
【年(卷),期】2018(29)19
【摘要】柔性的电子设备可直接贴附于人体皮肤,用于监测心跳、血压。
但是在实际应用中,庞大的外部电池会因为体积过大、供电不足或者噪声干扰等因素阻止设
备的长期运行。
近日,来自日本RIKEN研究所、东京大学的研究团队成功地突破这一瓶颈,研发出一款超弹性的生物传感器,由超薄的太阳能电池供电。
在动物试验中,这一创新设备可以应用于自供电的心脏监测器,精确、持续地监测心跳等生物信号。
相关文章于2018年9月26日在《Nature》上发表。
【总页数】1页(PF0002-F0002)
【关键词】电池供电;人体皮肤;监测器;心脏;科学家;《Nature》;电子设备;生物传感器
【作者】郭琳
【作者单位】
【正文语种】中文
【中图分类】R540.4
【相关文献】
1.贴在皮肤上的健康监测器 [J], 克里斯托弗·米姆斯;蒋青(翻译);
2.科学家发明能贴在皮肤上的“创可贴”MP3 [J],
3.Nature:开发出一种贴在皮肤上的自供电心脏监测器 [J],
4.科学家研发出可以贴在植物上的小型石墨烯传感器 [J], 材料牛
5.美国科学家发明能贴在皮肤上的“创可贴MP3” [J],
因版权原因,仅展示原文概要,查看原文内容请购买。
Rigid Body Cable for Virtual EnvironmentsMartin Servin and Claude Lacoursie`reAbstract—The present paper addresses the real-time simulation of cables for virtual environments.A faithful physical model based on constrained rigid bodies is introduced and discretized.The performance and stability of the numerical method are analyzed in detail and found to meet the requirements of interactive heavy hoisting simulations.The physical model is well behaved in the limit of infinite stiffness,as well as in the elastic regime,and the tuning parameters correspond directly to conventional material constants.The integration scheme mixes the well-known Sto¨rmer-Verlet method for the dynamics equations with the linearly implicit Euler method for the constraint equations and enables physical constraint relaxation and stabilization terms.The technique is shown to have superior numerical stability properties in comparison with either chain-link systems or spring and damper models.Experimental results are presented to show that the method results in stable real-time simulations.Stability persists for moderately large fixed integration step ofÁt¼1=60s,with hoisting loads of up to105times heavier than the elements of the cable.Further numerical experiments validating the physical model are also presented.Index Terms—Hoisting cable,interactive simulation,virtual environment,multibody system dynamics,elasticity,numerical stability, numerical integration.Ç1I NTRODUCTIONV IRTUAL environments(VE)are interactive visual simula-tions enabling experiences that may be difficult,costly, dangerous,or just impossible to realize in practice. VE-based systems are used extensively in commercial applications such as heavy machine operator or surgeons training systems,for instance.VEs are also used in applications ranging from robotics,early-stage virtual prototyping,and interactive entertainment,to name just a few.Fast physics integrators are also useful in molecular dynamics and other areas of basic scientific research.Robust visual simulations of real-world phenomena at interactive rates require both efficient numerical methods and expressive physical models compatible with each other. There is increasing demand both for increased speed, stability,and efficiency,and for increased modeling expressiveness.Rigid multibody systems dynamics[35]is a funda-mental component of physics-based VEs.Both the litera-ture and the software offering for rigid multibody system have reached some level of maturity.There are many software packages available for simulating these systems. Techniques for more complex physical systems such as deformable solids,fluids,and granular materials,among many others are actively developed.There are several introductory textbooks[11],as well as monographs, research papers,and review articles available.Realism in VEs depends more strongly on the global preservation of invariants such as energy and momentum,for instance,than on local accuracy of trajectories.This contrasts with the canonical wisdom of numerical analysis,where higher order methods are favored.Indeed,higher order methods are usually more stable and allow larger integration step,still providing very good local accuracy.They usually do less work for given accuracy and stability requirements. However,this is not necessarily true if the user inputs are unpredictable or nonsmooth,since higher order methods have to be restarted at each discontinuity.If one strives for maximum stability for the minimum work per step,as well as a predictable workload,a stable one-step one-stage fixed time-step method[14]is the best choice.In addition,high-order integration methods do not necessarily guarantee global bounds on the fluctuation of physical invariants. Unless one uses an energy preserving or a symplectic method,the value of energy could increase or decrease monotonically over time.However,variational integration methods,even the merely consistent ones such as the symplectic Euler scheme,do provide global bounds on energy fluctuation and exactly preserve a discrete momen-tum[18].For a mechanical system,a global bound on energy fluctuations corresponds to a stability guarantee as well.The focus of the present paper is the simulation of cables used in hoisting devices for VEs.These are used in simulator applications involving cranes of different types. Hoisting cables are often made of steel wires though chains are also used.Simulation of hoisting cables in VEs is subject to a number of slightly conflicting requirements,as listed in Section1.1.There is no previously existing combination of physical model and numerical method fulfilling all these requirements,motivating the new physical model and computational techniques presented herein.1.1Requirements for Hoisting CableThe requirements for simulation of hoisting cables in a VE application are now listed:1.Real time.The simulation should run in real time ata fixed rate of60Hz to integrate with standardVE applications..M.Servin is with the Department of Physics,Umea˚University,SE-90187Umea˚,Sweden.E-mail:martin.servin@physics.umu.se.. coursie`re is with the Department of Computing Science,Umea˚University,SE-90187Umea˚,Sweden.E-mail:claude@cs.umu.se.Manuscript received13June2007;revised24Oct.2007;accepted26Nov.2007;published online4Dec.2007.Recommended for acceptance by M.C.Lin.For information on obtaining reprints of this article,please send e-mail to:tvcg@,and reference IEEECS Log Number TVCG-2007-06-0067.Digital Object Identifier no.10.1109/TVCG.2007.70629.1077-2626/08/$25.00ß2008IEEE Published by the IEEE Computer Society2.Stability.Variations of energy should be globallybounded,and the bound should be moderatelysmall,of the order of a few percent.3.High mass ratios.Real hoisting cables can hold uploads more than10,000times their own weight.4.Physical elasticity.Parameterization of elasticityparameters for stretching,bending,and torsionshould correspond directly to known physical data.5.High stiffness.Heavy hoisting cables are extremelystiff with respect to stretching,bending,and torsion.6.Scene interaction.The virtual cable should interactwith other objects usually found in VE scenes vianonpenetration constraints generating dry frictionalcontacts or explicit attachments to rigid bodiesrepresenting pulleys,hooks,winches,trolley systems,etc.,using kinematic constraints.Requirement1can be met using a fixed integration step ofÁt¼1=60s%16:67ms,provided the computational time required to perform a single step is considerably smaller thanÁt.Variable time step or multiple smaller steps are possible,but only if the total wall clock computational time is still withinÁt for all steps.Also,a higher order method might not be compatible with the discontinuities due to impacts or dry friction,and this is another reason to prefer one-step single-stage fixed-step integration strategies. Requirement2can be met by using a variational integrator [18]and in view of requirement1,a first-order method should be chosen.When constraints are used,either a mixed strategy[20]or a purely variational strategy[21]can be used,as long as it includes physical constraint relaxation and stabilization.These integration methods of Lacoursie`re make it possible to meet requirement4as well.In this paper, we use a somewhat simplified integration method that is not fully symplectic for nonzero relaxation.For zero relaxation, our method reduces to the SHAKE[14]integrator,which is symplectic.For nonzero relaxation,however,the proposed integrator is slightly dissipative,and the additional terms provide constraint stabilization with strong linear stability. In effect,the integrator gives globally bound energy,as ing a lumped element model based on rigid bodies ensures compliance with requirement6.The large mass ratio requirement3is specific to hoisting cable.In combination with the requirement5of stiff elasticity,the equations of motion become particularly stiff and many of the methods widely used in computer graphics—spring-and-damper models in particular—are ruled out because of stability issues or for lack of a direct correspondence between simulation parameters and physi-cal properties.Since available VE frameworks largely build on efficient techniques for rigid body simulation,the requirements1and6suggests that also cables should be modeled as lumped elements,using rigid body components.1.2Previous WorkAn overview of the dynamics and control of cranes is not presented here but is found in the literature[1].When it comes to simulation,most common crane models do not include any dynamics for the cable.In some applications, the cable is included as a single stiff spring of variable length or modeled by a single kinematic constraint between the load and the hoisting structure.In more elaborate models[15],[19],the hoisting dynamics is derived from a kinematic constraint acting simultaneously on the crane construction,trolleys,and loads,maintaining a given total length of the cable.We also extended such models in a previous paper[29]to include resistance to cable twisting motion and cable elasticity.None of the strategies cited above include the cable represented by a physical body,and thus,these do not allow full-scale interaction between the cable and other objects in a VE via contacts,for instance.There are few examples of real-time simulations for VEs involving dynamics cable models—presumably due to the difficulty in producing fast and stable simulations for these for large stiffness—and no examples of hoisting of heavy loads.Cables are examples of deformable physical bodies. These can be simulated using finite elements,lumped elements,or modal models.Both lumped and finite element models have been used to simulate cables.A short review of these applications is now provided with an emphasis on models and methods that have been applied to interactive simulation.A simulation model using finite elements[10]based on the Cosserat model,including stretching,torsional,and bending energy[26],was found to be efficient as long as connection points are restricted at the extremities of the cable,thus limiting interactivity.Lumped element models couple simple physical bodies such as point particles or rigid bodies with penalty forces or constraints.A rigid body model was used for the simulation of antenna booms carried by space shuttles[7].Systems of point masses connected with spring-damper forces have been reported,modeling either stretching[16]or both stretching and bending[23].Note however that particle models do not allow torsion that is needed in the simulation of hoisting. Lumped point mass element models of Cosserat rods including stretching,bending,and torsional elasticity has been presented in[13]and[31].The bending and torsion is included by augmenting the point mass system by assigning the intermediate segments a rotational state.This extends the system degrees of freedom to that of a cable modeled by lumped rigid bodies and the equations to be integrated in time are precisely the Newton-Euler equations of motion.These papers present no validation of the models or performance for high-mass ratios.There are also other strategies based on point particles and penalty forces proportional to displacements from a reference configura-tion,either by defining restoring forces for volume,surface, or linear distortion[28],[32],or using a global corotated shape matching strategy[24].Models based on penalty forces have limitations with regards to stiffness;however, this can be alleviated to some degree by using an implicit numerical integrator[25],though the computational cost for this is similar to that of solving for a constrained system.Lumped elements can be coupled using kinematic constraints also.It is possible to simulate a perfectly rigid chain by connecting rigid bodies with hinges of alternating rotation axis for ing standard methods of robotics[35]such a chain can be made perfectly rigid and can be a good starting point for cable models of cranes[17]. The resulting cable is then perfectly inelastic however and cannot account for stretching dynamics at all.If one uses a descriptor form of the constrained equations of motion (also referred to as the Lagrange multiplier method), solving explicitly for the constraint forces,exact constraint satisfaction can be relaxed.The descriptor formulation isadvantageous because of the unified treatment of non-holonomic constraints and loop closure constraints.It has the same linear complexity as the recursive formulation of robotics for linear chains provided sparsity is exploited in the linear systems of equations.In addition,the descriptor formulation allows for constraint relaxation,which is not possible with recursive or reduced coordinate methods of robotics.However,using standard constraint stabilization techniques[3],[4],[5],[9],it is not possible to map the relaxation parameters to the physical parameters.This is remedied with the technique in Section2.Multibody systems subject to constraints are more ex-pensive to simulate than those involving only explicit forces. Recent papers suggest that it is possible to achieve linear or even logarithmic complexity with enough parallelism[12], [27]by exploiting a level-of-detail strategy.A related method showing linear complexity in both number of elements and number of contacts is presented in[34].The difficulty in achieving stable real-time simulation, including a dynamical cable model for the hoisting of heavy weights(more than10-100times the cable mass)is not covered in any of the cited work above because of limitations on stiffness or mass ratios.To our knowledge, there is no existing method that meets the requirements for hoisting cable in VEs listed in Section1.1.1.3Our ContributionsThe contributions of this paper to the modeling and computation of cable dynamics for VEs are the following. We formulate a cable model as a chain of rigid bodies connected with a new type of angular constraint.This constraint is formulated in terms of the joint center,as well as the bend and twist angles about it.A regularization technique is used to allow constraint relaxation and to associate energy with constraint violation.In the stiff limit, the new constraint is just one form of rigid locking.However, the configuration is designed to parameterize the degrees of freedom as they appear in elasticity theory when the constraint is relaxed.This provides a direct connection to elasticity theory.With the chosen integration method, described in Section2.2,the relaxation parameters can be safely set to zero,corresponding to rigid constraints.For nonzero relaxation,our experiments validate the model, as the force-displacement relations match those predicted by the theory.We demonstrate the stability of the time stepping scheme of Section2.2at step sizeÁt¼1=60s and for mass ratios up to105for rigid body ing a particle model that includes bending energies,the mass ratio can be arbitrarily high,provided that the bending energy is scaled adequately to suppress transversal high-frequency oscilla-tions.We argue that the bending and torsional forces have a stabilizing effect on the system,and we present an analysis of the mechanism at work here.It should be emphasized that the elastic forces described cannot be included as explicit forces but must be computed as regularized constraints in order to achieve stability for the range of parameters covered.Integration can be made efficient by recognizing the strongly banded structure of the Schur complement—the matrix involved in the linear equation to be solved at each time step.The remaining loop-closing constraints result in a few off-diagonal blocks.The system is solved using a block preconditioned Gauss-Seidel solver,where the cable block is solved using a direct fixed bandwidth solver,and the couplings between the cable and other objects are computed using Gauss-Seidel iterations.The computational performance of the simulation depends linearly on the number of cable elements.Although we focus on hoisting cable,the method we present is of general use for the graphics community. Constraint regularization can improve the numerical stability of any simulation of systems with stiff interactions,and the angular constraint in particular can be applied to any (Cartesian-coordinate)constraint-based articulated body solver.The constraint method itself can handle branching and closed loops efficiently and with linear complexity provided a good sparse solver is used such as UMFPACK[33]. Finding an optimal strategy for closed loops is an ongoing research and will be published elsewhere.The rest of the paper is organized as follows:Essential notions of multibody dynamics in descriptor form are presented in Section2,which contains the integration method in Section 2.2.Several alternative models to simulate cables with relaxed constraints are presented in Section3,and experiments are performed on these to determine the most stable ones.Elements of elasticity theory for cables are then presented in Section4.A preconditioned Gauss-Seidel solver that uses grouping and splitting is then presented in Section6.Results of model validation and numerical stability experiments are presented in Section7. Example applications are discussed in Section8,followed by a summary and conclusions in Section9.2M ULTIBODY D YNAMICSThe following notations are used in what follows.Unlessexplicitly stated,all quantities are expressed in a global inertial frame.The state vector of the multibody system of N rigid bodies isðq T;v TÞT.The partitioned vector q¼ðq Tð1Þ;q Tð2Þ;...;q TðNÞÞT contains the generalized coordinatevectors qðiÞ¼ðx TðiÞ;e TðiÞÞT,where xðiÞis the center of mass position vector of bodyðiÞ,and eðiÞis a unit quaternion defining the orientation of the body.The velocities arerepresented by v¼ðv Tð1Þ;v Tð2Þ;...;v TðNÞÞT,where vðiÞ¼ð_x TðiÞ;!TðiÞÞT for bodyðiÞand with the angular velocity vector denoted by!ðiÞ.With these representations,we have the relation_qðiÞ¼TðqðiÞÞvðiÞ,where TðqðiÞÞ¼diagð13Â3;~TðeðiÞÞÞ, 13Â3is the3Â3identity matrix,and~TðeÞ¼12Àe1Àe2Àe3e0e3Àe2Àe3e0e1e2Àe1e0B B@1C CA:ð1ÞThe body mass mðiÞand inertia tensor IðiÞ,expressed in the inertial frame are collected into the mass matrix MðiÞ¼diagðmðiÞ13Â3;IðiÞÞ.The mass matrix of the entire system is then M¼diagðMð1Þ;Mð2Þ;...;MðNÞÞ.The bodyframe inertia tensor is I0ðiÞso the inertia tensor in theinertial frame is IðiÞ¼RðiÞI0ðiÞR TðiÞ,where RðiÞ¼RðiÞðeðiÞÞis the rotation matrix of bodyðiÞ.SERVIN AND LACOURSI ERE:RIGID BODY CABLE FOR VIRTUAL ENVIRONMENTS785The multibody system then satisfies the Newton-Euler equations of motion:M _v ¼f M þf;ð2Þwhere f represents internal and external forces and f M ¼À_Mvis the gyroscopic force.For each rigid body ði Þ,we can read off the equation M ði Þ_vði Þ¼f M ði Þþf ði Þ,where f M ði Þ¼À_Mði Þv ði Þ.The Newton-Euler equations are discre-tized and integrated to produce the discrete trajectories at fixed time intervals.1These are then used to drive the three-dimensional (3D)graphics display.2.1Potentials and ConstraintsThe internal interactions are modeled with potential forces and kinematic constraints.The potential energy of the system is U ðq;t Þ,and the corresponding force is f ¼ÀT T @U=@q T .For stiff systems,subject to strong elastic and dissipative forces varying significantly on comparatively short time scales,it is particularly difficult to find numerical integrators that are fast,stable,and faithful to the physics.As an alternative approach to standard implicit integration,strong forces are here considered as weakly relaxed kinematic constraints—a form of regularization.Mathematically,a constraint restricts the coordinates to lie on a surface ðq;t Þ¼0in configuration space.That surface can be time dependent.The corresponding constraint force that acts to keep the coordinates q ðt Þon the surface ðq;t Þ¼0is f c ¼J T ,where J ¼ð@ =@q ÞT ðq Þis the constraint Jacobian and ,the Lagrange multiplier.The constraint force acts in a direction normal to the constraint surface.The constraint force amplitude is here seen as dynamical variable,and the equations of motion are no longer a set of ordinary differential equations (ODE),but instead,they form a set of differential algebraic equations (DAEs)with the inclusion of the algebraic equation ðq;t Þ¼0.Differentiating the constraint ðq;t Þ¼0with respect to time yields 0¼_¼Jv þ@t .Therefore,time-dependent constraints,assuming that Jv ¼0,exert theinstantaneous rate of work f Tcv ¼ T Jv ¼À T ð@ =@t Þon the system.For a system with N c constraints,we use the representa-tion ¼ð T 1½ ; T ½2 ;...; T½N c ÞT ,where ½i is the i th constraint with dimension d ½i and involves any number of bodies.Thedimension of is thus dim ð Þ¼Pi d ½i d c .The dimension of the system Jacobian is then dim ðJ Þ¼d c Â6N ,and the dimension of the Lagrange multiplier is dim ð Þ¼d c .Unless a coordinate reduction strategy is used,con-straints are never exactly satisfied during numerical integration and the constraint violation —the euclidean norm j j —has a finite value and dynamics of its own.There are various well-known techniques to stabilize constraint violation [3],[4],[5],[9].Our choice is a physical constraint regularization and stabilization scheme [20],in which constraints are made explicitly compliant and thus allowed to oscillate,and then strongly damped using only physical terms added to the Lagrangian formulation.In thisframework,constraints are replaced by stiff potentials,butthe DAE form of the system is retained;so,the variables are solved for directly and discretized independently of the other variables.We may represent the system potential asU ðq Þ¼12T ðq Þ"À1 ðq Þð3Þfor some real non-negative diagonal matrix ",of dimension d c Âd c ,that has the role of inverse stiffness of the potential.The contribution to the generalized force of this potential takes the formf ¼ÀJ T "À1 :ð4ÞNote that if the artificial variable is introduced as ¼À"À1 ,the generalized force can be written f ¼J T ,and the equations of motion are modified to the following DAE system:_q¼T ðq Þv;ð5ÞM _vÀJ T ¼f M þf;ð6Þ" ðq;t Þ¼À ðq;t Þ:ð7ÞIn this formulation,we may choose between making theconstraint entirely stiff by setting "¼0without any singularities in (5)and (7)or working with finite stiffness.A stiff force representation without the would not have a well-behaved limit as "!0.For finite regularization ">0,the constraint forces are linear restorations of stiffness 1=",directly proportional to the constraint violation.Strongdamping can also be added by substituting ! þ _in the right-hand side of (7),with a damping coefficient >0.The effective damping coefficient for constraint oscillations is then =",and this damping also behaves nicely as "!0when the discretization of Section 2.2is used.2.2Numerical IntegrationWe use a mix of the symplectic and linearly implicit Euler methods for the numerical integration of the system of (5)-(7).The symplectic Euler method,also known as Sto¨rmer-Verlet,has good properties with respect to global preservation of the invariants of physical systems [14].This makes it a natural choice when symplecticity and preserva-tion of global invariants are of higher importance than high local accuracy.Symplectic Euler is used for the dynamics variable on the first line of the equations of motion (5).The second line is the discretized using the implicit Euler formula of first order because that equation is assumed to be stiff.The same combination was used in the context of real-time simulation of deformable bodies previously [30].Symplectic Euler discretization of the system (5)-(7)and Taylor expansion ðx n þ1Þ¼ n þÁtJ n v n þ1þO ðÁt 2Þgives the following first-order time stepping algorithm:q n þ1¼q n þÁtT ðq n Þv n þ1;ð8ÞA n u n þ1¼b n ;ð9ÞwhereA n ¼M n ÀJ TnJ nÁt À2";ð10Þand u n þ1¼ðv T n þ1;Át T n þ1ÞT ,b n ¼ðMv T n þÁtf T n ;ÀÁt À1 T n ÞT,and the gyroscopic force f M is included in f from here on.786IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS,VOL.14,NO.4,JULY/AUGUST 20081.An alternative approach is to make a time discretization of the Lagrangian for the system and impose a discretized least action principle.Numerical integrators derived this way are referred to as variational integrators,and these can be constructed to preserve invariants of the system.See [18]for further details.The matrix A n is typically block sparse.The linear system of equations may be solved by first building the Schur complement,S JM À1J T þÁt À2",solve for the Lagrange multiplier fromS ¼ÀÁt À1Jv ÀJM À1f ÀÁt À2ð11Þand then compute the velocity v n þ1by direct substitutionand finally update the positions.Observe that there is no singularity for "¼0that can be made arbitrarily small,as long as the Jacobian matrix J has full row rank.In addition,for finite ">0,the linear system is well posed,and it is well conditioned as long as the rows of J and M are not badly scaled.3N UMERICAL S TABILITY E XPERIMENTS OFP ARTICLE -B ASED C ABLESThe double pendulum is well known to become numeri-cally ill-conditioned for large mass ratios.We thus investigate how the N-link pendulum may be stabilized by adding supplementary constraints between heavy or static components and lighter elements.An illustration of the configurations considered in the following numerical experiments is found in Fig.1.Of course,regularization can be applied to any of the different models.The main question we strive to answer here is whether stability can be increased by simultaneously relaxing constraints cou-pling the lighter elements and strengthening the constraints between the heavier ones,usually found at each end of a cable.The physical idea behind this is to let constraints between the elements of similar mass take most of the heavy load.Numerically,this corresponds to equilibrating the scaling of the rows of the Schur complement matrix S .The reason for performing numerical experiments to evaluate stability is that we suspect that constraints nonlinearity and finite precision arithmetic play determin-ing roles,and neither issues are addressed satisfactorily with a linear stability analysis.For the systems at hand,the N particles are indexed by i .The heavy load has index i ¼N and mass M i ¼M ,and the light elements have index i <N and mass M i ¼m .The rest state separation length between the particles are denoted by d ,and the total length is L ¼Nd .The models considered are illustrated in Fig.1,and the constraints for each case are as follows:1.link chain (pairwise distance constraints)¼ð d 0;...; d N À1ÞT ;0¼ d i j d i j Àd ;2.link chain enforced by a massless cable constraint [29](a total length preservation constraint)¼ð d 0;...; d N À1; m ÞT ;0¼ d i j d i j Àd;0¼ mX N i ¼1j d i j ÀL ;3.link chain with load enforcement (an extra link for direct support of the load)¼ð d 0;...; d N À1; le ÞT ;0¼ d i j d i j Àd;0¼ le j x ðN Þj ÀL ;4.truncated link chain enforced by a massless cable constraint (the bottom most link being removed)¼ð d 0;...; d N À2; m ÞT ;0¼ d i j d i j Àd;0¼ mX N i ¼1j d i j ÀL ;5.link chain with angular constraint (the chain link keptat straight angles)¼ð d 0; a T 0;...; d N À2; a TN À2; d N À1ÞT ;0¼ d i j d i j Àd;0¼ a i arctan ðj d i Âd i þ1j ;d i Ád i þ1Þ;where d i ¼x ði þ1ÞÀx ði Þ,and x ð0Þis the constant position of the pendulum anchor point.We use the atan2function such that the bend angle, a i ,ranges between ðÀ ; Þ.The Jacobian blocks areJ d ii ¼ÀJ d ii þ1¼Àd ij d i j;ð12ÞJ m ¼X N i ¼1...;d i j d i j ;...;Àd ij d i j ;... ;ð13ÞJ a i ðJ a ii ;J a ii þ1;J a ii þ2Þ¼d Ád Âþd ÁA Àj d Âjd Âþd ÁB ;ð14ÞSERVIN ANDLACOURSI ERE:RIGID BODY CABLE FOR VIRTUAL ENVIRONMENTS787Fig.1.Illustration of the link chain configurations considered.The red curve represents constraints supplementary to the pairwise distanceconstraints.The purpose of the supplementary constraints is to increase the numerical stability of the system.These supplementary constraints are (b)-(d)massless cable and (e)angular constraint.。