VIBRO_1_DIRECT_simulations-ACTRAN振动声学直接频响分析理论

Vibro-Acoustic SimulationsACTRAN Training – VIBROCopyright Free Field TechnologiesIntroductionPre-requisites - before going through this presentation, the reader should have read and understood the following presentations:1_BASICS_General_Program_Organization.pdf; Workshop_BASICS_0_Edit_an_ACTRAN_input_file.pdf.These slides present the basics materials, components and boundary conditions involved in a structural simulation in physical coordinates.2Copyright Free Field TechnologiesContentThe structural MaterialsThe visco-elastic and shell ComponentThe equivalent beam Component and MaterialThe discrete Component and MaterialThe Boundary ConditionsMeshing Criteria3Copyright Free Field TechnologiesStructural MaterialsThe solid materials are used for describing both viscous and non viscous solids with and without different structural properties along the different axisThree different types solid materials are available:Isotropic solid material Transverse isotropic solid material Orthotropic materialComposite materials can also be defined to model the different layers of a solid material using a homogenization option – See dedicated presentation4Copyright Free Field TechnologiesThe Isotropic Solid Material (1)Isotropic materials are materials whose mechanical properties are uniform along all directionsThe properties that define an Isotropic solid material can be given using 2 set of parameters:Young modulus (E) Poisson ratio (ν) Solid density or First (λ) Lamé’s coefficient and Second (µ or G, the shear modulus) Lamé’s coefficient Solid densityAll parameters are mandatory5Copyright Free Field TechnologiesThe Isotropic Solid Material (2)Syntax in the ACTRAN input file:BEGIN MATERIAL Id ISOTROPIC_SOLID YOUNG_MODULUS value POISSON_RATIO value SOLID_DENSITY value END MATERIAL IdOrDefinition in ACTRAN/VIBEGIN MATERIAL Id ISOTROPIC_SOLID LAME1 value LAME2 value SOLID_DENSITY value END MATERIAL Id6Copyright Free Field TechnologiesThe Transverse Isotropic Solid Material (1)Transverse isotropic materials are materials whose mechanical properties are symmetric about an axis that is normal to a plane of isotropy.Unidirectional fiber composite lamina; Honeycomb components, …The properties that define a transverse isotropic solid material are:5 mechanical properties En, νn, Et, νt and G; Solid density Axis of isotropy, oriented along the fibers3 2 1 7Copyright Free Field TechnologiesThe Transverse Isotropic Solid Material (2)Their mechanical properties can be divided in different parts:Young modulus (En) and Poisson ratio (νn) when sujected to normal (along the isotropy axis) load (also named normal_E and normal_ν) Young modulus (Et) and Poisson ratio (νt) when sujected to transverse (along the isotropy plane) load (also named inplane_E and inplane_ν) Shear modulus (G) characterizing inplane shear deformations due to shear loads The isotropy axis defining the direction of the fiber in the local coordinate system8Copyright Free Field TechnologiesThe Transverse Isotropic Solid Material (3)Syntax in the ACTRAN input file: Definition in ACTRAN/VIBEGIN MATERIAL Id TRANSVERSE_ISOTROPIC_SOLID NORMAL_E_MODULUS value INPLANE_E_MODULUS value NORMAL_POISSON_RATIO value INPLANE_POISSON_RATIO value NORMAL_S_MODULUS value ISOTROPIC_AXIS value SOLID_DENSITY value END MATERIAL Id9Copyright Free Field TechnologiesThe Orthotropic Solid Material (1)Orthotropic materials are materials whose mechanical properties are different in all directions:Honeycomb components; Wood,…The properties that define an orthotropic solid material are:9 Mechanical properties E1, E2, E3, ν12, ν13, ν23, G12, G13, G23; Solid density10Copyright Free Field TechnologiesE i corresponds to the Young modulus inthe direction i expressed in the local coordinate systemG ij corresponds to the shear modulus indirection i for which the shear load relies on the plane whose normal is in direction x 2x 3x 1x 2x 3SNN/E 1-ν12 N/E 1-ν12 N/E 1j in the local coordinate system (G ij =G ji ) νij is the Poisson ratio that corresponds toa contraction in direction j when an extension is applied in direction IThe local coordinate system is defined bythe element and the component that refers to an orthotropic materialx 1S/G 13S/G 13SS/G 23S/G 23x 1x 2x 3Syntax in the ACTRAN input file: Definition in ACTRAN/VI BEGIN MATERIAL IdORTHOTROPIC_SOLIDYOUNG_1 valueYOUNG_2 valueYOUNG_3 valuePOISSON_12 valuePOISSON_13 valuePOISSON_23 valueSHEAR_12 valueSHEAR_13 valueSHEAR_23 valueSOLID_DENSITY valueEND MATERIAL IdDamping ModelAll properties in ACTRAN are defined using complex numbersDamping can be introduced using a complex Young modulus:withE’ the Young modulus, image of the stiffness"'jE E E +=E” the Loss modulus, representing internal lossesThe loss modulus is linked to the internal loss factor η(also called tg(δ)) by:()ηj E jE E E +⋅=+=1'"'ContentThe structural MaterialsThe visco-elastic and shell ComponentsThe equivalent beam Component and Material The discrete Component and MaterialThe Boundary ConditionsMeshing CriteriaThe Solid component is the standardSupported topologies component for modeling visco-elastic solid parts.Points to a valid Isotropic solid materialUnknowns: solid displacement in each direction –3 dofs per node (no rotation)Syntax in the ACTRAN input file:Definition in ACTRAN/VIBEGIN COMPONENT IdSOLIDMATERIAL material_id [POWER_EVALUATION 1][INCOMPRESSIBLE 1]END COMPONENT IdPOWER_EVALUATION 1 activatesthe computation of the dissipated power in the component (optional) INCOMPRESSIBLE 1 allows to modelvisco-elastic parts with a Poisson ratio close to 0.5 (optional -check the ACTRAN Users’ Manual for more information)Choose “Solid” as typeDomainThe solid shell component is used to modelSupported topologies transverse solid element, with a thicknessdirectionOne dimension of the structure should be smallcompared to the 2 others (roughly 1/15)Thickness (and thus compression effects) areaccounted for using solid shellsIts formulation converges faster for thin structuresthan a solid componentCan point to all solid materials (isotropic,transverse isotropic, orthotropic, composite)Unknowns: solid displacement in each direction –3 dofs per node (no rotation)Syntax in the ACTRAN input file:POWER_EVALUATION 1 activates theDefinition in ACTRAN/VIBEGIN COMPONENT IdSHELL [AUTO_ORIENT]MATERIAL material_id [POWER_EVALUATION 1][REFERENCE_DIRECTION 1 0 0]END COMPONENT Idcomputation of the dissipated power in the component (optional) REFERENCE_DIRECTION allows toorient the local material coordinate system for non isotropic solid materials (default 1,0,0) AUTO_ORIENT keyword allows toautomatically reorient the transverse direction of the elementsChoose “Solid Shell” as typeDomainShell elements’ orientation is an important parameter (transverse direction)The transverse direction is dependent of the order of the nodes in the element description (input file, MESH > ELEMENT) :BEGIN ELEMENT ...212 12 112 13 14 15 27 28 29 30...END ELEMENTLower nodes Upper Nodes1213141527282930Meshes obtained by normal extrusion or normal sweeping lead to a correct numbering (lower nodes then upper nodes)Automatic detection is possible using the keyword AUTO_ORIENT .This remark is valid for all transverse elements: Solid Shell, ViscothermalAUTO_ORIENT should automatically detect the transverse direction of theshell elementDimensions close to be the same…hazardous AUTO_ORIENTThe Thin Shell Component (1)The thin shell component is used to model transverse thin elementOne dimension of the structure should be small compared to the 2 others (roughly 1/15) Thickness specification is mandatory Formulation is similar to the NASTRAN CQUADR and TRIAR Supported topologies31 243Can point to all solid materials (isotropic, transverse isotropic, orthotropic, composite)1 2Unknowns: solid displacement and rotation in each direction – 6dofs per nodeRemark: only linear elements are supported21Copyright Free Field TechnologiesThe Thin Shell Component (2)Syntax in the ACTRAN input file:BEGIN COMPONENT Id DSHELL MATERIAL material_id THICKNESS thickness [OFFSET offset] [POWER_EVALUATION 1] [LUMPED_MASS 0,1,2] [REFERENCE_DIRECTION 1 0 0] END COMPONENT IdDefinition in ACTRAN/VITHICKNESS value is mandatory, while the OFFSET can be optional POWER_EVALUATION 1 activates the computation of the dissipated power in the component (optional) REFERENCE_DIRECTION allows orienting the local material coordinate system for non isotropic solid materials (default 1,0,0)22Copyright Free Field TechnologiesDomainChoose “Thin Shell” as typeLumped Mass FormulationThe lumped mass formulation is a simplified formulation:Mass matrix only contains diagonal translational components (no rotational components) This formulation should decrease the computation time, but should converge slower than the standard formulation (this is not always true)The Lumped Mass formulation is NOT selected by default (different from NASTRAN)23Copyright Free Field TechnologiesSolid Shell Elements: Application(Glaverbel/Splintex)Glass layersPVB layer PVB24Copyright Free Field TechnologiesContentThe structural MaterialsThe visco-elastic and shell ComponentThe equivalent beam Component and MaterialThe discrete Component and MaterialThe Boundary ConditionsMeshing Criteria25Copyright Free Field TechnologiesThe Beam Material (1)Beam_inertia materials are used to define equivalent stiffeners mechanical properties using inertia indicators Inertia indicators can usually be retrieved in external tools or from analytical solutionsThe following properties are needed:The solid density and area of the beam cross-section The elongation modulus represent the stiffness in the z’-axis The inertia XX corresponds to the inertia with respect to the rotation around the y’ axis (=I1 in Nastran) The inertia YY corresponds to the inertia with respect to the rotation around the x’ axis (=I2 in Nastran) The inertia XY corresponds to the product inertia The inertia Z corresponds to the torsionnal inertia The cg offset values represent the position of the center of gravity (neutral axis) within the local coordinate system (default = 0) The shear offset values represent the position of the shear center within the local coordinate system (default = 0) The shear factor values represent shear stiffness factors K in K*A*G. They adjust in this way the effective transverse shear cross-section area (default = 1)Offsets and inertia are oriented within the local coordinate system of the beam element26Copyright Free Field TechnologiesThe Beam Material (2)Syntax in the ACTRAN input file:BEGIN MATERIAL material_id BEAM_INERTIA ELONGATION_MODULUS value SHEAR_MODULUS value SOLID_DENSITY value AREA value INERTIA_XX value INERTIA_XY value INERTIA_YY value CG_OFFSET_X value CG_OFFSET_Y value SHEAR_FACTOR_X value SHEAR_FACTOR_Y value SHEAR_OFFSET_X value SHEAR_OFFSET_Y value INERTIA_Z value END MATERIAL material_idDefinition in ACTRAN/VI27Copyright Free Field TechnologiesThe Beam Component (1)The Beam component is used to model equivalent stiffeners on thin elementsFormulation is similar to the NASTRAN CBEAM The component allows orienting spatially a specific beam type Supported topologiesVrefCan only point to a beam_inertia materialX’Z’Unknowns: solid displacement and rotation in each direction – 6dofs per nodeRemark: only linear elements are supportedY’28Copyright Free Field TechnologiesThe Beam Component (2)Syntax in the ACTRAN input file:BEGIN COMPONENT Id BEAM MATERIAL id [REFERENCE_DIRECTION cx cy cz] [POINT_REF 1] [POWER_EVALUATION 1] END COMPONENT IdDefinition in ACTRAN/VIcx, cy and cz are defining a reference vector which defines the local x axis Point ref to one allows to define the local system by specifying the coordinates of a point (in vref) The local element coordinate system (x’,y’,z’) is defined as follows:axis z’ is defined by the two nodes on which the beam is constructed; axes x’ and y’ are defining a plane normal to axis z’ axes x’ is defined by the projection of the reference vector on this plane; axis y’ is computed in such a way that (x’,y’,z’) form a direct orthonormal system By default, without definition of vref, the normal to the shell element is taken as the x’ axisDomain29Copyright Free Field TechnologiesContentThe structural MaterialsThe visco-elastic and shell ComponentThe equivalent beam Component and MaterialThe discrete Component and MaterialThe Boundary ConditionsMeshing Criteria30Copyright Free Field TechnologiesSpring material is the standard material for specifying stiffnesses and masses associated to node-to-ground springs, node-to-node springs or lumped masses (described by a discrete component)A free combination of stiffnesses and masses can be specified:Either in absolute coordinates (along X, Y and Z);Or in local coordinates (transverse and normal directionSyntax in the ACTRAN input file: Definition in ACTRAN/VI BEGIN MATERIAL material_idSPRINGeither[NORMAL_STIFFNESS stiff_n][TRANSVERSE_STIFFNESS stiff_t]or[X_STIFFNESS stiff_x][Y_STIFFNESS stiff_y][Z_STIFFNESS stiff_z]end eithereither[NORMAL_MASS mass_n][TRANSVERSE_MASS mass_t]or[X_MASS mass_x][Y_MASS mass_y][Z_MASS mass_z]end eitherEND MATERIAL material_idThe Discrete component is used to model node-to-ground or node-to-node springs. Additionally,they may also be used to model lumped massesThe behavior depend on the element type (1D or 0D) and the material properties Supported topologies **ttNode-to-ground (point)Syntax in the ACTRAN input file:cx , cy and cz are defining theDefinition in ACTRAN/VIBEGIN COMPONENT IdDISCRETEREFERENCE_DIRECTION cx cy cz [POWER_EVALUATION 1]END COMPONENT Idnormal direction if not straightforward (on an edge) POWER_EVALUATION 1activatesthe computation of the dissipated power in the component (optional)DomainContentThe structural MaterialsThe visco-elastic and shell ComponentThe equivalent beam Component and Material The discrete Component and MaterialThe Boundary ConditionsMeshing CriteriaBoundary ConditionsDeterministic boundary conditions :Displacement based boundary-conditionsRotational based boundary conditionsPoint, distributed and mechanical pressure loadStochastic boundary conditions (see dedicated presentation): Diffuse sound fieldTurbulent boundary layerDelta correlated (Rain on the roof)Deterministic Boundary ConditionsDisplacement :BEGIN DISPLACEMENTNumber of fixed nodesNode number, displacement component values or FREE END DISPLACEMENTRotation :BEGIN ROTATIONNumber of fixed nodesNode number, rotation component values or FREEEND ROTATION Point load :BEGIN POINT_LOADNumber of loaded nodesNode number, load component valuesEND POINT_LOADPoint moment :BEGIN POINT_MOMENTNumber of loaded nodesNode number, load component valuesEND POINT_MOMENTDistributed load :BEGIN DISTRIBUTED_LOADNumber of loaded facesFace definition, distributed load component valuesEND DISTRIBUTED_LOADPressure load :BEGIN DISTRIBUTED_PRESSURENumber of loaded facesFace definition, distributed pressure valuesEND DISTRIBUTED_PRESSUREStructural Boundary ConditionsSolid elements:Degrees of freedom ACTRAN = displacement in 3 directions (3 dofs/node) Default: free displacementThin elements:Additionally 3 rotational dofs (Default: free rotation)Ideal cases:clampedsimply supportedSolid shellThin shellConstrained displacement Constrained rotationContentThe structural MaterialsThe visco-elastic and shell ComponentThe equivalent beam Component and Material The discrete Component and MaterialThe Boundary ConditionsMeshing CriteriaFluid / Structure CouplingThe structural and acoustic components can be coupled to perform vibro-acoustic simulations. Three configurations are possible.Weak coupling where no retro-action of the fluid on the structure is taken into account Acoustic and structures model are 2 decoupled problems. Theacoustic model is excited from the structural results. The BC_MESH feature is used (see dedicated presentation).Strong coupling. The retro-action of the fluid is taken into account and the acoustic and structure components are in the same model. The acoustic and structure components can have compatible or incompatible meshes.In case of compatible meshes (the nodes at the interface are shared) the coupling is automatically detected by ACTRAN and taken into accountIn case of incompatible meshes the coupling must be specified by the user through an INTERFACE data block (see dedicated presentation).Output QuantitiesThe main quantities that can be output on structural components are: Local quantities (at field points or storage node)•The solid rotation (vector) codes srx,sry,srz•The solid displacement (vector) codes sux,suy,suzGlobal quantities (on domains) :•Length (scalar) code lgt•Mean Square Solid Velocity (scalar) code mv•Mean Square Solid Normal Velocity (scalar) code mnv•Mass (scalar) code mass•Squared Solid Normal Velocity (scalar) code snv•Squared Solid Velocity (scalar) code sv•Volume (scalar) code vol•Surface (scalar) code srfMeshing CriteriaAcoustic: Determine the acoustic wavelength as the ratio of the sound speed by the frequency Apply the following rule: use a minimum of • 6 linear elements per wavelength • 4 quadratic elements per wavelength The higher the frequency, the smaller the wavelength, the smaller the max min 44f c h ==λGoing FurtherThe concepts that have been presented are put in practice in the workshop Workshop_VIBRO_1a_Direct_Freq_Res.pdfThe different vibro-acoustic couplings methods are introduced in VIBRO_2_Fluid_Structure_Coupling.pdf。