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造纸专业英文词汇〔新〕paper：纸tissue：薄页纸sheet：纸页paperweb：纸幅basepaperforcorrugatedboard：瓦楞纸板原纸untrimmedwebwidth：抄宽，毛纸宽trimmedwebwidth：切边后纸幅宽度trimstripwidth：切边宽度〔复卷机，切纸机〕operatingspeed〔ofmachine〕：〔纸机〕抄速machinewidth：机宽paperboard，cardboard，board：纸板pulp，stock，stuff：浆，浆料pulppreparing，stockpreparation：备浆perfectstuff：符合规定配比的纸浆chemicalpulp：化学浆groundwood：磨木浆chest：浆池〔stock〕tank，trough，：〔浆〕池，槽vat：槽，浆槽sump，storage：贮〔油、液〕槽，集〔油〕池dumpchest：卸料池clogging：堵塞，堵浆coarsescreenings，ejects：浆渣reject，rejects，rejectedstock，rejections，ejects：筛渣，浆渣junk:垃圾，废料tailings：尾浆，浆渣stockfraction，lump：浆团shive，〔stock〕bolts，stick，clottedfiber：浆块dragspot，fiberchumps：浆疙瘩waterandfiberbalance：浆水平衡junkbox〔trap，collector〕：废料槽，废料箱，废料收集器pulper：碎浆机，水力碎浆机operation：工作原理，操作，运行maintenance：维护lubrication：润滑install，attach，assemble：安装，装配，架设detach：拆卸mount：安装，架设dismountable：可拆卸的tearing〔breaking〕strength：撕裂度tensileproperties，tensilebreakingstrength：抗张强度tension：张力〔stock，pulp，stuff〕consistency：浆浓fillerretention：填料的留着率filler，fillings，loadingmaterial：填料ashcontent：灰分impacttester：冲击强度测定仪wetstrength：湿强度airpermeability：透气度，透气性airpermeabilitytester：透气度测定仪burst，burstingstrength，popstrength：耐破度burstfactor：耐破因子fold：折叠foldingendurance，foldingstrength：耐折度foldingresistance：耐折性能bendingstiffness：弯曲曲折折挺度smoothness：平滑度contactangletest：〔施胶度〕接触角测定法whiteness：白度absorbability：汲取性能opacity，opaqueness：不透明度diaphanometer：不透明度测量仪ringcrushcompressionresistance：环压强度ringstiffness：环压挺度flatcrushresistance：平压强度〔瓦楞芯纸〕acidfastness：耐酸度acidresistance：耐酸性能，耐酸强度beater：打浆机beatingdegree：打浆度SR：肖氏打浆度Canadianfreenessstandard(CFS,cfs)：加拿大标准游离度Canadianstandardfreenesstester：加拿大标准游离度测定仪basisweight，grammage：定量，克重〔specific〕gravity：比重bendstrength：弯曲曲折折强度bendingchip：耐折叠纸板bendingfatiguetester：弯曲曲折折疲惫性能测定仪wind，winding：卷纸winder，rewinder：卷纸机，复卷机unwind，unreeling：退纸unwinder，unreelingstand，unwindingstand，backstand：退纸架unwindroll：退纸的纸卷unroll：纸卷退纸unwinddiameter：退纸纸卷直径rewinddiameter：复卷纸卷直径axialregulation：轴向调节radialregulation：径向调节oscillationpath：振动路径naturalbrowns：本色牛皮纸浆paperboardgrade〔stock〕：纸板用纸浆flutingpaper，corrugatedpaper：瓦楞纸papermaking：抄纸，造纸pulpandpapertechnology：制浆造纸工艺AOCC：美国旧瓦楞纸，美国进口废纸〔Americanoldcorrugatedcase〕Aflute：A级瓦楞纸波形数〔每30厘米36±3个〕Bflute：B级瓦楞纸波形数〔每30厘米51±3个〕Cflute：C级瓦楞纸波形数〔每30厘米42±3个〕abieteneacid：松香酸absolutedry，bonedry(B.D.,b.d.)，ovendry(O.D.,o.d.)：尽对干度〔尽干〕airdry(A.D.,a.d.)：风干〔含水量20%〕absolutehumidity：尽对湿度acceptedstock：合格浆料，良浆accept：合格品，良浆mechanic：钳工，技工technician：技术员criticalpart：要紧构件，要害部件pronze：阳极化〔防腐〕处理reducer：减速箱，传动箱gearreducer：齿轮减速箱wormgear：蜗轮clutch：离合器coupling：联轴器，轴接，偶联bevelgear：歪齿轮，伞形齿轮tooth：齿牙heel：歪齿轮的大端toe：齿牙的齿顶mate：啮合，配合matinggear：啮合齿轮，配套的齿轮carbide-tipped：〔头上镶有碳化物〕硬质合金的switchgear：开关齿轮bearing：轴承bearMagainstN：把M靠〔压〕在N上bearingcap：轴承盖，轴承套sleeve〔bracket〕bearing：轴承套toothbearingareas：〔齿轮的〕齿牙承载区域taperedrollerbearing：滚锥轴承，锥形滚柱轴承innerrace：〔滚动轴承的〕内座圈，内环outerrace：〔滚动轴承的〕外座圈，外环retainingring：扣〔卡、承托〕环，挡圈washer，spacer，gasket，insert，shim：垫片，垫圈flinger：抛油环〔圈〕snapring：开口环，弹性挡环labyrinthring：迷宫〔圈，环〕sling：吊环contamination：污染，杂质additive：添加剂aging：老化，返黄yellowing：返黄artificialaging：人工老化airdeckle：气控定边器doctor：刮刀airdoctor：气刀airknife：气刀analyticalbalance：分析天平anglecoder：角度编码器approachflow〔ofstock〕：〔浆料〕上网approachflowsystem〔纸机上的〕流浆系统pulper，aquapulper，hydrapulper：水力碎浆机batchtypehydrapulper：间歇式水力碎浆机arcfoil：弧形案板，弧形胶脱水板ash，ashcontent：灰分，灰分含量aspectratio：纵横比assembly：机组，成套设备，联动装置，基团averagefiberlength：纤维平均长度dryer：烘缸backliner：纸板芯层，纸板衬层backside，driveside：：传动侧，传动面foreside，serviceside，tendingside，tenderside：操作侧，操作面backtender：枯燥工backtenderhelp：压光工backwater，whitewater：回水，白水weakwhiteliquor：稀白液strong〔thickened〕whitewater：浓白水baffle：挡板，挡水板，挡浆板baleopener：拆包机bibliometer：吸水性能测定仪biologicaloxygendemand〔BOD〕：生物耗氧量chemicaloxygendemand〔COD〕：化学耗氧量blackliquor：黑液blottingcapacity：吸墨性能cellularboard，corrugatedboard：瓦楞纸板board，paperboard：纸板linerboard：挂面纸板liningboard：衬里纸板notestboard=non-testboard：低耐破度纸板krafttestliner：牛皮纸箱纸板，高耐破度硫酸盐纸板packagingboard：包装用纸板packingboard：垫圈纸板bottomcouchroll：下伏辊bowedroll，cheeseroll，curvedbarspreader，curvedroll，spreaderroll：弧形辊，弓形辊，伸展辊bowl：纸粕辊〔超级压光机〕break：断纸，断头breakresistance：抗断裂性能breakinglength：裂断长breastboard：胸板breastbox：网前箱breastroll：胸辊brightness：亮度broke：损纸waste：废〔纸〕，废〔水〕brooming：帚化bulgeresistance：〔纸板〕抗破裂度bulk：松厚〔度〕bunchtubeflowbox：束管式流浆箱converfloheadbox：层流式流浆箱burst：破裂〔度〕，耐破度bursttester，burstingtester：耐破度测定仪cadytest：耐破度测定calender：压光机calender〔water〕box：压光机水匣calenderbowl：压光辊calendersection：压光部calendertrain：压光机组calenderstack：压光辊组caliper，thickness：厚度camberedroll，crownedroll：中高辊crowncontrolledroll：可控中高辊capitalrepair：大修overhaulandrepair:大修与小修maintenance:维护,维修downtime：〔工厂、机器等由于维修或待料等的〕停工期fillet：纸幅接头，镶边，接头carrierdrum：复卷机底辊，支承辊carrierroll：导网辊coating：涂布coater：涂布机coatings：涂料centriclone，centrifugalcleaner，centricleaner，cyclean：锥形除渣器centriffler：两段除渣器centrifiner：立式除渣器centri-sorter：旋翼筛chainconveyer：链式运输机，链板机check：检查，核对checkdamper：风挡checkplate：挡板checkvalve，clackvalve，non-returnvalve：单向阀，止逆阀chuck：夹盘，夹头chute：歪槽，送料槽clearcutting：净切边clearance：刀距，间隙〔papermachine〕clothing：造纸机珍贵器材〔指毛毯、铜网、塑料网等〕coarsescreen：粗筛finescreen：细筛flatscreen，jogstrainer：平筛，平板筛浆机slot/hole：筛缝/筛孔coarsescreenings，ejects：浆渣cofferdam：白水沟堰板conditioner：毛毯洗涤器，调节器conditioning：调整处理，调湿consistencytransmitter：浓度传感器coolingcylinder，coolingdrum：冷缸spacing:间隔，空隙core：纸芯corrugatedroll：沟纹辊corrugating：起瓦楞corrugator：瓦楞成形机corrugatorroll：瓦楞辊couch：堰伏，伏辊couchbreak：伏辊断头couchfelt，couchjacket，couchrolljacket：伏辊毯〔套〕couchpit：伏辊坑pit：坑，池，纹孔couchpress，couchroll：伏辊couchsquirt：伏辊水针couchvacuuntranfer：伏辊真空引纸装置coucher：伏辊，伏辊工cutter：切纸机cylinder：缸，圆网drycylinder：烘缸dampeningroll，dampingroll：润湿辊dancer〔roll〕：压纸辊dancingroll：导纸辊threading：领纸，引纸guideroll：校正辊，导辊dandyroll：水印辊deadknife：固定刀decker：浓缩机deckle：定边装置，定幅装置featheredge：毛边featheredgedeckle：定边带intermittently：间歇地defiber，defibrize，defibering，defibration：纤维不离deflake：碎解，分层〔片〕，剥片knead：揉搓flank：侧面，后面defoam：消泡dehydrate，dewater：脱水cooking，digesting：蒸煮distributorroll：〔涂料〕分配辊，匀浆辊evenerplate：匀浆板evener〔roll〕：匀浆辊perforation：筛孔，钻孔perforationplate：匀浆板，多孔板perforator：匀浆辊holeyroll，holyroll：整流辊，匀浆辊draping：换网drivenroll：从动辊drivenshaft：从动轴dryline：水线dryend，dryingnest，dryersection，dryerpart：枯燥部dumpingvalve，emptyingvalve：放料阀，放浆阀ejectvalve：排渣阀enteringreel：待裁切纸卷，待退纸卷enrichedwater：浓白水fab-foil：曲曲折折面案板，弧面脱水板foil：案板facewire，facingwire：外网，面网innerwire：里网，衬网fastbeating：游离状打浆slowbeating，wetbeating：粘状打浆feed，feeding：喂料，喂浆feeder：喂料器feedback：相应feedforward：前馈felt：毛毯，毛布feltside：毛毯面，正面feltstretcher：毛毯张紧器，毛毯张紧辊fiberfurnish，paperformulation：纤维配比，配浆比率proportioner，proportioningbox：配浆箱pulpcontent：纸浆配比，纸浆含量furnish：配料fiberpick：纤维起毛pick：粘辊，掉毛，掉粉pickfelt：引纸毛毯pickroll：引纸辊pickerroll：疏散辊filler：填料fillerretention：填料留着率finishedroll：成品纸卷finishedweight：净重，纸卷重量finishing：整饰，完成fitter：装配工flowapproach：流浆系统，浆料流送系统flowbox：流浆箱，网前箱flowchart，flowdiagram，flowsheet：流程图flowcontrol：流量操纵flowdistributer，flowevener：整流器，匀浆器，匀浆辊flowmeter：流量计hygrometer：湿度计kinemometer：流速计manometer：〔液体〕压力计pressuregauge，pressuremeter：压力表micrometer：厚度计，测微计pathmeter：测厚计viscometer，viscosimeter：粘度计flowontowire：浆料上网flowsensor：流量传感器flyingsplice：纸幅机上连续粘接flyingpaster：纸幅自动接头anchorscrew，footscrew：地足螺丝anchorstud：地足螺栓lockscrew：锁紧螺丝eyescrew：环首螺丝allenscrew：六角固定螺丝setscrew：固定螺丝Loctite，Locktite：螺丝紧固剂grout：灌浆〔水泥地板〕distortion：变形，变态，失真pivot-point：支点，中心点form，forming：〔纸页〕成形formingbox：成形箱formingdrum，formingroll：成形辊formingsection，formingsector：成形区，成形部formingshoe：弧面成形板formingtable，fourdriniertable：网案fourdrinier：长网造纸机fourdrinierpart，fourdriniersection：网部fourdrinierwetend：湿部fractionator：筛分仪fractionation：分级，筛分tertiary〔screen〕：三级〔筛〕quartiary：四级〔筛〕freerun：空运转run-in，testrun：对…试车，试运转freewater：游离水freshwater：清水glazing，gloss：光泽的，光泽groovedroll：沟纹辊hatch：人孔，升落孔headtank：高位槽housing：罩，套in-linebasisweightcontroller：机上定量操纵装置in-linemoisturecontroller：机上水分含量操纵装置inkabsorbency：吸墨性能kraft：牛皮纸，硫酸盐浆，牛皮浆bleach：漂白unbleachedpulp〔stock〕：未漂浆laminater，laminator：层压机leadingroll：导纸辊leadingstrips，leadingthroughtape，tail：引〔领〕纸纸条lickup，licking，tailthreading：引纸lick-upfelt：引纸毛毯tailshooter：切纸水针jack：千斤顶liftingdevice：提升装置，起吊装置lifting，hoist，elevation：提升，起吊longdirection，longitudinal，machinedirection：纵向〔的〕crossdirection：横向cross-machine：machinedirection：纸机纵向loweringdevice，lowerator：〔卷筒纸〕落落装置lubrication：润滑machinepit，wirepit：〔纸机〕白水坑manostat：恒压器，稳压器mesh：网目monitor：监测器，班组长nip：压区niproll：光泽辊nominal：额定的，公称的，标称的rated：额定的optimum：最优化的，最正确的paddle：浆叶，搅拌叶padding：衬垫papercarryingroll：引纸辊paperspringroll：导纸弹簧辊papercore：纸芯管paperroll：卷筒纸pinadhesion：〔瓦楞纸板〕面层与芯层的粘合强度pneumatic：气动的hydraulic：液压的ventilation：通风pressfeltconditioner：压榨毛毯洗涤器presspart〔section〕：压榨部preparationofstock：备浆，浆料处理pressuredifferential：压差pressuredrop，reliefpressure：压落pressureloss：压损procedure：过程，工艺过程，方法，程序，步骤process：过程，方法profile：外形，轮廓，全幅profilecaliper〔thickness〕：全幅横向厚度reel：纸轴，纸卷，卷筒纸，卷纸refine：精磨，精制，磨浆refiner：磨浆，精磨机，精浆机guard〔s〕：平安罩，防护装置regulate，adjust：调节right〔left〕handmachine：右〔左〕rotor：转子rotorblade〔vane〕：转子叶片filling:转子叶片，耐磨片stator：定子，底刀ripper：纵切机slitter：纵切机，纵切刀rollset：卷筒纸边缘卷曲曲折折rubbercoveredroll：包胶辊rubber-lined，rubberlining：橡胶衬里的separator：捕沙器，捕沙沟saveall：白水回收器，白水回收装置saveallbox〔pan，tray〕：白水槽〔盘〕shavings，trimmings：纸边strip：窄条，吹提，解吸，〔真空吸水箱的〕密封条strips：纸条sheave，pulley：皮带轮，滑轮steplesscontrol：无级操纵，连续操纵shower：喷水，喷水管〔器〕screen，sueve：筛子size，sizing：胶料，涂胶，施胶sizeresistance，sizingdegree：施胶度light〔soft,slack〕sized：轻度施胶sleeve，socket：套管，套slide〔sliding〕valve：滑阀span：跨距，跨度spareparts：备件critialpart：要紧部件，要害部件spraycutter，squirt，squirtcut，tailcutter：水针trimshower，trimsquirt：水针nozzlecutter：切边水针stainlesssteel：不锈钢mildsteel：低碳钢normally-closed：常〔原〕位闭合的，常闭的starch：淀粉bus：〔电器〕总线，terminal：端子，端部，接头，线端stretcher：张紧辊stretch：伸长〔率〕suction：吸水suctionbabypress：真空预压榨suctionbreastroll：真空胸辊suctioncouch〔roll〕，vacuumcouch：真空伏辊supervisor：治理人，主管table：表，网案，tableroll：案辊torque，moment：扭力矩，转力矩momentofinteria：惯性矩，转动惯量fork-lift，forklifttruck：叉车，铲车troubleshooting：排除故障defect，trouble，malfunction：故障tangential：切线的，切向的V-belt：V形皮带，三角皮带conical，taper：锥形的ventilation：通风upright，vertical：立式的horizontal:水平的,卧式的watershed：〔网上〕纸幅水线，分水界线watershedoffset：水线偏差watermark：水印，罗纹wrongside：〔纸幅〕网面，反面yield：得率withrespectto：关于woodfree：不含磨木浆的interlock：联锁partialload；局部荷载stuffingbox：密封盒，填料盒sling：吊环snapring；开口环labyrinthring；迷宫环〔圈，垫〕locknut，jamnut：锁紧〔锁定，防松〕螺帽annex：附加，附带，附件massrejectrate：浆渣重量比例airend:冷却风机〔用于空压机中〕airreliefvalve：减压阀，平安阀accessdoor：检修门，人孔门dustcap：防尘盖dualcontrol：二分操纵〔空压机自动操纵系统〕quadrocontrol：四分操纵IP：〔大气〕防护等级uhlebox：〔真空〕吸水箱adjustorstript：〔真空箱的调节吸水宽度的密封条〕SymBelt TM roll：靴压辊〔二压的上辊〕shoe：靴套，belt皮套Sym-ZLroll：〔二压下辊〕talcpowder：滑石粉overheadcrane：行车，吊车rigof“port-a-bar〞type：手动葫芦lub.shower：润滑喷水管wet/det.shower：定湿喷水管snatchblock：紧线(扣绳)滑轮nodulariron:球墨铸铁heavygrade:陡坡,大坡airspring:气垫hysteresis:滞后作用fabricroll网辊Breastroll胸辊WALKWAYOFCHAINCONVERYOR链板机走道造纸专业英文词汇paper：纸tissue:薄叶纸sheet:纸页paperweb:纸幅untrimmedwidth:抄宽，毛纸宽machinewidth:机宽paperboard;cardboard;board:纸板pulp;stock;stuff:浆，浆料pulppreparing:备浆perfectpulp:符合规定配比的纸浆chemicalpulp:化学浆groundwood:磨木浆chest:浆池(stock)tank;trough;:〔浆〕池，槽vat:槽，浆槽sump;storage:贮〔油、液〕槽，集〔油〕池clogging堵塞，堵浆coarsescreenings;ejects:浆渣reject;rejects;rejectedstock;rejections;ejects:筛渣，浆渣junk:垃圾，废料tailings:尾浆，浆渣junkbox(trap;collector):废料槽，废料箱，废料收集器pulper:碎浆机，水力碎浆机wind;winding:卷纸winder;rewinder:卷纸机，复卷机unwind;unreeling:退纸unwinder;unreelingstand;unwindingstand:退纸架unwindroll:退纸的纸辊untroll:纸卷退纸naturalbrowns:本色牛皮纸浆paperboardgrade(stock):纸板用纸浆flutingpaper;corrugatedpaper:瓦楞纸papermaking:抄纸。
节选-ABAQUS帮助文档翻译 reference to: user manual 18.62008-10-10 12:5918.6 理解自适应网格（adaptive meshing）自适应网格可以通过移动独立的材料网格(allowing the mesh to move independently of the material),让你在整个分析过程中即使发生大变形，也能保持高质量的网格。
通常自适应网格只移动节点，网格的拓扑并不改变。
注意：通常自适应网格多用在Dynamic （动态分析），Explicit and Dynamic（显示动态分析）, Temp-disp, Explicit 中。
定义模型中某个区域采用自适应网格的设置：other-->Adaptive Mesh Domain 自适应网格的选项控制设置:Other--〉Adaptive Mesh Controls 通常，在每一个step中只能有一个自适应网格区域。
21.2.1 ABAQUS/Standard defines contact between two bodies in terms of two surfaces that may interact; these surfaces are called a “contact pair.”ABAQUS/Standard defines “self-contact,” which is available only in two-dimensional analysis, in terms of a single surface. [if gte vml 1]><![endif][if !vml][endif]Figure 21.2.1–1 Contact and interaction discretization. 从the first surface (the “slave” surface)的节点向the second surface (the “master” surface)做垂线，寻找最近的垂线的垂足，The interaction is then discretized between the point on the master surface and the slave node. Strict master-slave contact 在这种关系下，主面的节点可以穿入从面（副面），但副面不可以穿入主面。
workbench中⽂⼀、Definition1.Stiffness behavior (刚度特性）Flexible (灵活的）rigid（刚性）Gasket (垫⽚）2.suppressed（抑制）3.Coordinate system（坐标系统）Default Coordinate system （缺省坐标系统）4.Reference Temperature（参考温度）⼆、Material1.Assignment（分配）2.Nonlinear Effects（⾮线性效应）3.Thermal Strain Effects （热应变影响）三、Properties（性质）1.centroid（质⼼）2.Moment of Inertia IP1 (转动惯量）四、Statistic（统计）1.Mesh Metric（⽹络指标）⼀、Definition1.Element Control（元素掌控）Program Controlled（受控程序）Manual（⼈⼯，⼿动）2.Display Style （显⽰样式）Body ColorPart ColorMaterialNonlinear Material Effects Stiffness Behavior⼆、Properties （性质）1.scale Factor value（⽐例因⼦的值）三、Basic Geometry Options （基本⼏何选项）1.Parameters （参量）2.Parameter key（主要参数）3..Attributes（特性）/doc/2451a0457********edb11e9.html d Selections （按名称选择）5.Material Properties（材料属性）四、Advanced Geometry Options （⾼级⼏何选项）/doc/2451a0457********edb11e9.html e Associativity（使⽤结合性）2.Reader Mode Saves Updates File（读者模式保存更新⽂件）/doc/2451a0457********edb11e9.html e Instances（使⽤实体实例）4.Smart CAD Update（智能CAD更新）5.Attach File Via Temp File（附加⽂件通过临时⽂件）6.Temporary Directory（暂时⽬录）7.Analysis Type（分析类型）8.Decompose Disjoint Faces9.Enclosure and Symmetry Processing （外壳和对称处理）⼀、Definition1.TypeCartesian（笛卡尔）Cylindrical （圆柱形）2.Coordinate System（坐标系）Program Controlled（受控程序）Manual（⼿动，⼈⼯）Coordinate System ID（坐标系统ID）⼀、Scopｅ1.Scoping MethodGeometry Selection（⼏何选择）Named Selection（名称选择）⼆、Definition1.Type2.Scope Mode3.Behavior4.Suppressed三、Advanced1.Formulation（调配）Program ControlledAugmented Lagrange（⼴义拉格朗⽇法）Pure Penalty（罚函数法）MPC（微程式控制）Normal Lagrange（拉格朗⽇法）2.Detection MethodProgram ControlledOn Gauss Point（在⾼斯点）Nodal-Normal From Contact （从接触）Nodal-Normal to Target（⽬标节点正常）Nodal-Projected Normal From Contact （从接触结点预计正常）3.Normal Stiffness（法向刚度）4.Update Stiffness（更新刚度）Never Each Iteration（每次迭代）Each Iteration,Aggressive5.Pinball Region（弹球区域）Auto Detection ValueRadius（半径）。
造纸专业英文词汇（新）pulp，stock，stuff：浆，浆料pulp preparing，stock preparation：备浆chemical pulp：化学浆chest：浆池（stock）tank，trough，：（浆）池，槽vat：槽，浆槽sump，storage：贮（油、液）槽，集（油）池dump chest：卸料池clogging：堵塞，堵浆coarse screenings，ejects：浆渣reject，rejects，rejected stock，rejections，ejects：筛渣，浆渣junk:垃圾，废料tailings：尾浆，浆渣water and fiber balance：浆水平衡operation：工作原理，操作，运行maintenance：维护lubrication：润滑install，attach，assemble：安装，装配，架设detach：拆卸mount：安装，架设dismountable：可拆卸的ring crush compression resistance：环压强度ring stiffness：环压挺度bending fatigue tester：弯曲疲劳性能测定仪absolute dry，bone dry(B.D.,b.d.)，oven dry(O.D.,o.d.)：绝对干度（绝干）air dry(A.D.,a.d.)：风干（含水量20%）mechanic：钳工，技工technician：技术员critical part：主要构件，要害部件reducer：减速箱，传动箱gear reducer：齿轮减速箱worm gear：蜗轮clutch：离合器coupling：联轴器，轴接，偶联bevel gear：斜齿轮，伞形齿轮tooth：齿牙heel：斜齿轮的大端toe：齿牙的齿顶mate：啮合，配合mating gear：啮合齿轮，配套的齿轮carbide-tipped：（头上镶有碳化物）硬质合金的switchgear：开关齿轮bearing：轴承bear M against N：把M靠（压）在N上bearing cap：轴承盖，轴承套sleeve （bracket）bearing：轴承套tooth bearing areas：（齿轮的）齿牙承载区域tapered roller bearing：滚锥轴承，锥形滚柱轴承inner race：（滚动轴承的）内座圈，内环outer race：（滚动轴承的）外座圈，外环retaining ring：扣（卡、承托）环，挡圈washer，spacer，gasket，insert，shim：垫片，垫圈flinger：抛油环（圈）snap ring：开口环，弹性挡环labyrinth ring：迷宫（圈，环）sling：吊环contamination：污染，杂质artificial aging：人工老化air deckle：气控定边器doctor：刮刀assembly：机组，成套设备，联动装置，基团back side，drive side：：传动侧，传动面fore side，service side，tending side，tender side：操作侧，操作面back tender：干燥工weak white liquor：稀白液strong（thickened）white water：浓白水baffle：挡板，挡水板，挡浆板biological oxygen demand（BOD）：生物耗氧量chemical oxygen demand（COD）：化学耗氧量breast board：胸板capital repair：大修overhaul and repair:大修与小修maintenance:维护,维修downtime：（工厂、机器等由于维修或待料等的）停工期cyclean：锥形除渣器centriffler：两段除渣器check：检查，核对check damper：风挡check plate：挡板check valve，clack valve，non-return valve：单向阀，止逆阀coarse screenings，ejects：浆渣consistency transmitter：浓度传感器spacing:间隔，空隙pit：坑，池，纹孔dead knife：固定刀decker：浓缩机intermittently：间歇地defoam：消泡dehydrate，dewater：脱水cooking，digesting：蒸煮dry line：水线feed，feeding：喂料，喂浆feeder：喂料器feedback：反馈feedforward：前馈finishing：整饰，完成fitter：装配工flow approach：流浆系统，浆料流送系统flow box：流浆箱，网前箱flow chart，flow diagram，flow sheet：流程图flow control：流量控制flow distributer，flow evener：整流器，匀浆器，匀浆辊flow meter：流量计hygrometer：湿度计kinemometer：流速计manometer：（液体）压力计pressure gauge，pressure meter：压力表anchor screw，foot screw：地脚螺丝anchor stud：地脚螺栓lock screw：锁紧螺丝eye screw：环首螺丝allen screw：六角固定螺丝set screw：固定螺丝Loctite，Locktite：螺丝紧固剂grout：灌浆（水泥地板）distortion：变形，变态，失真free run：空运转run-in，test run：对…试车，试运转fresh water：清水hatch：人孔，升降孔head tank：高位槽housing：罩，套in-line basis weight controller：机上定量控制装置bleach：漂白unbleached pulp（stock）：未漂浆jack：千斤顶lifting device：提升装置，起吊装置lifting，hoist，elevation：提升，起吊long direction，longitudinal ，machine direction：纵向（的）cross direction：横向cross-machine：lubrication：润滑manostat：恒压器，稳压器mesh：网目monitor：监测器，班组长nominal：额定的，公称的，标称的rated：额定的optimum：最优化的，最佳的pneumatic：气动的hydraulic：液压的ventilation：通风pressure differential：压差pressure drop，relief pressure：压降pressure loss：压损procedure：过程，工艺过程，方法，程序，步骤process：过程，方法guard（s）：安全罩，防护装置regulate，adjust：调节rotor：转子rotor blade（vane）：转子叶片filling: 转子叶片，耐磨片stator：定子，底刀rubber-lined ，rubber lining：橡胶衬里的saveall box（pan，tray）：白水槽（盘）sheave，pulley：皮带轮，滑轮stepless control：无级控制，连续控制shower：喷水，喷水管（器）screen，sueve：筛子sleeve，socket：套管，套slide（sliding）valve：滑阀span：跨距，跨度spare parts：备件critial part：主要部件，要害部件spray cutter，squirt，squirt cut，tail cutter：水针trim shower，trim squirt：水针stainless steel：不锈钢mild steel：低碳钢normally-closed：常（原）位闭合的，常闭的bus：（电器）总线，terminal：端子，端部，接头，线端suction：吸水supervisor：管理人，主管torque，moment：扭力矩，转力矩moment of interia：惯性矩，转动惯量fork-lift，forklift truck：叉车，铲车trouble shooting：排除故障defect，trouble，malfunction：故障tangential：切线的，切向的V-belt：V形皮带，三角皮带conical，taper：锥形的ventilation：通风upright，vertical：立式的horizontal:水平的,卧式的yield：得率with respect to：关于interlock：联锁partial load；部分荷载stuffing box：密封盒，填料盒sling：吊环snap ring；开口环labyrinth ring；迷宫环（圈，垫）lock nut，jam nut：锁紧（锁定，防松）螺帽annex：附加，附带，附件massreject rate：浆渣重量比例airend:冷却风机（用于空压机中）air relief valve：减压阀，安全阀access door：检修门，人孔门dust cap：防尘盖dual control：二分控制（空压机自动控制系统）quadro control：四分控制IP：（大气）防护等级uhle box：（真空）吸水箱talc powder：滑石粉overhead crane：行车，吊车rig of “port-a-bar”type：手动葫芦lub. shower：润滑喷水管snatch block：紧线(扣绳)滑轮nodular iron: 球墨铸铁hysteresis:滞后作用pulp; stock; stuff: 浆，浆料pulp preparing: 备浆perfect pulp:符合规定配比的纸浆chest:浆池(stock) tank; trough;:（浆）池，槽vat:槽，浆槽sump; storage:贮（油、液）槽，集（油）池clogging堵塞，堵浆coarse screenings; ejects:浆渣reject; rejects; rejected stock; rejections;ejects:筛渣，浆渣junk:垃圾，废料tailings:尾浆，浆渣absolute dry; bone dry(B.D.; b.d.); oven dry(O.D.; o.d.):绝对干度（绝干）air dry(A.D.; a.d.):风干（含水20%）sheave; pulley:皮带轮，滑轮stepless control:无级控制，连续控制smoothness:平滑度shower:喷水，喷水管（器）screen; sueve:筛子sleeve, socket:套管，套slide (sliding) valve:滑阀span:跨距spare parts:备件critial part:主要部件，要害部件stainless steel:不锈钢mail steel:低碳钢normally-closed:常（原）位闭合的，常闭的starch:淀粉bus:（电器）总线terminal:端子，端部，接头，线端supervisor:管理人，主管torque; moment:扭力矩，转力矩moment of interia:惯性矩，转动惯量fork-lift; forklift truck:叉车，铲车trouble shooting:排除故障defect; trouble; malfunction:故障tangential:切线的，切向的V-belt:V形皮带，三角皮带conical; taper:锥形的ventilation:通风upright; vertical:立式的nominal:额定的，公称的，标称的rated:额定的optimum:最优化的，最佳的padding:衬垫pneumatic:气动的hydraulic:液压的ventilation:通风press felt conditioner:压榨毛毯洗涤器press part (section):压榨部preparation of stock:备浆，浆料处理pressure differential:压差pressure drop; relief pressure: 压降pressure loss:压损procedure:过程，工艺过程，方法，程序，步骤process:过程，方法profile:外形，轮廓，全幅refine:精磨，精制，磨浆regulate; adjust:调节right (left) hand machine:右（左）手机ring crush compression resistance:环压强度ring stiffness:环压挺度rotor:转子rotor blade(vane):转子叶片stator:定子，底刀ripper:纵切机slitter:纵切机，纵切刀rubber-lined, rubber lining:橡胶衬里的separator:捕沙器，捕沙沟saveall:白水回收器，白水回收装置saveall box (pan, tray):白水槽（盘）shavings, trimmings:纸边strip:窄条，吹提，解吸strip：纸条fractionator:筛分仪fractionation:分级，筛分tertiary(screen):三级（筛）free run:空运转run-in, test run:对…试车，试运转free water:游离水fresh water;清水glazing; gloss:光泽的，光泽hatch:人孔，升降孔head tank:高位槽housing:罩，套impact tester:冲击强度测定仪kraft:牛皮纸，硫酸盐浆，牛皮浆bleach:漂白unbleached pulp(stock):未漂浆laminater, laminator:层压机jack:千斤顶lifting device: 提升装置long direction; longitudinal; machine direction:纵向（的）cross direction:横向cross-machine:纸机横向lowering device; lowerator:（卷筒纸）降落装置lubrication:润滑machine pit; wire pit:（纸机）白水坑manostat:恒压器，稳压器mesh:网目monitor:监测器，班组长nip:压区nip roll:光泽辊felt stretcher:毛毯张紧器，毛毯张紧辊fiber furnish; paper formulation:纤维配比，配浆比率furnish:配料fiber pick:纤维起毛filler:填料filler retention:填料留着率finishing:整饰，完成fitter:装配工flow approach:流浆系统，浆料流送系统flow chart; flow diagram; flow sheet:流程图flow control:流量控制flow meter:流量计hygrometer:湿度计kinemometer:流速计manometer:（液体）压力计pressure gauge, pressure meter:压力表micrometer：厚度计，测微计pathmeter:测厚计viscometer; viscosimeter:粘度计flow onto wire:浆料上网flow sensor:流量传感器flow indicator:流量计fold:折叠folding resistance:耐折性能anchor screw; food screw:地脚螺丝lock screw:锁紧螺丝eye screw:环首螺丝allen screw:六角螺丝set screw:固定螺丝pivot-point:支点，中心点dead knife:固定刀decker:浓缩机deckle:定边装置，定幅装置intermittently:间歇期defiber ; defibrize ; defibering; defibrartion:纤维分离deflake:碎解，分层（片），剥片knead:揉搓flank;侧面，后面defoam:消泡dehydrate; dewater:脱水diaphanometer:不透明度测量仪cooking; digesting:蒸煮distributor roll:（涂料）分配辊evener (roll):匀浆辊perforation:筛孔driven shaft:从动轴dry line:水线dry end; drying section; dryer part:干燥部dumping valve; emptying valve:放料阀eject valve:排渣阀enriched water:浓白水fab-foil:曲面案板，弧面脱水板foil:案板，耐磨板face wire; facing wire:外网，面网inner wire:里网，衬网feed; feeding:喂料，喂浆feeder:喂料器feedback:反馈feedforward:前馈check plate:挡板check valve, clack valve, non-return valve:单向阀，止逆阀chuck:夹盘，夹头chute:斜槽，送料槽clear cutting:净切边clearance:刀距，间隙clutch:离合器coupling:离合器，联结器，轴接，偶联coarse screen:粗筛fine screen:细筛，精筛flat screen; jog screen:平筛，平板筛浆机vibrancy screen:振动筛，跳筛slot/hole:筛缝/筛孔coarse screenings; ejects:浆渣conditioner:毛毯洗涤器，调节器conditioning:调整处理，调湿consistency transmitter:浓度传感器cooling cylinder; cooling drum:冷缸washer, spacer; gasket ; insert ; shim:垫片，垫圈flinger:抛油环（圈）spacing:间隙，空隙pit:坑，池，纹孔caliper:游标卡尺caliper rule:卡尺capital repair:大修(specific) gravity:比重bevel gear:斜齿轮。
帮助文件摘要：26.1.4In Abaqus/Standard section controls are used to select the enhanced hourglass control formulation for solid, shell, and membrane elements. This formulation provides improved coarse mesh accuracy with slightly higher computational cost and performs better for nonlinear material response at high strain levels when compared with the default total stiffness formulation. Section controls can also be used to select some element formulations that may be relevant for a subsequentAbaqus/Explicit analysis.In Abaqus/Explicit the default formulations for solid, shell, and membrane elements have been chosen to perform satisfactorily on a wide class of quasi-static and explicit dynamic simulations. However, certain formulations give rise to some trade-off between accuracy and performance. Abaqus/Explicit provides section controls to modify these element formulations so that you can optimize these objectives for a specific application. Section controls can also be used in Abaqus/Explicit to specify scale factors for linear and quadratic bulk viscosity parameters. You can also control the initial stresses in membrane elements for applications such as airbags in crash simulations and introduce the initial stresses gradually based on an amplitude definition.The enhanced hourglass control approach available in both Abaqus/Standard and Abaqus/Explicit represents a refinement of the pure stiffness method in which the stiffness coefficients are based on the enhanced assumed strain method; no scale factor is required. It is the default hourglass control approach for hyperelastic, hyperfoam, and low-density foam materials in Abaqus/Explicit and for hyperelastic, hyperfoam, and hysteresis materials in Abaqus/Standard. This method gives more accurate displacement solutions for coarse meshes with linear elastic materials as compared to other hourglass control methods. It also provides increased resistance to hourglassing for nonlinear materials. Although generally beneficial, this may give overly stiff response in problems displaying plastic yielding under bending. In Abaqus/Explicit the enhanced hourglass method will generally predict a much better return to the original configuration for hyperelastic or hyperfoam materials when loading is removed.The enhanced hourglass control method is available for first-order solid, membrane, and finite-strain shell elements with reduced integration. In Abaqus/Explicit it cannot be used for a hyperelastic or hyperfoam material when adaptive meshing is used on that domain (see the discussion below).The enhanced hourglass method cannot be used with elements modeled with hyperelastic or hyperfoam materials that are included in an adaptive mesh domain. Thus, if you decide to use hyperelastic or hyperfoam materials in an adaptive mesh domain, you must specify sectioncontrols to choose a different hourglass control approach. The use of adaptive meshing in domains modeled with finite-strain elastic materials is not recommended since better results are generally predicted using the enhanced hourglass method and, for solid elements, element distortion control (discussed below). Therefore, for these materials it is recommended that the analysis be run without adaptive meshing but with enhanced hourglass control.A1:有限元方法一般以节点的位移作为基本变量，单元内各点的位移以及应变均采用形函数对各节点的位移进行插值计算而得，应力根据本构方程由应变计算得到，然后就可以计算单元的内能了。
Editorial/AnnouncementCompetent 足以胜任的；有能力的；称职的；合格的Rotary 旋转的；绕轴转动的bio-inspired design 仿生设计aeroelasticity 空气弹性变性acoustics 声学；（房间、戏院的）传声效果expertise 专长；专门知识；专门技能fidelity 忠诚忠实尽责保真度multidisciplinary （涉及）多门学科的maneuverability n.可操作性；驾驶性能optimization 最佳的最优的最优化aeroelastic空气弹性变型的configurations 配置；结构；外形；布置demanding 要求高的；需要高技能（或耐性等）的；费力的；要求极严的constant 连续发生的；不断的；重复的；不变的Administrator （公司、机构的）管理人员In addition I want to express special thanks to the editors-in-chief of all other AIAA technical journals for constant communication and frequent help and advice.Thorough adj.彻底的；完全的；深入的；细致的thoroughness n.透彻完全Prompt 准时的及时的迅速的提示Reviews 评论；回顾；审查；检查Manuscripts 抄本原稿Potential 潜在的可能的Innovation 创新；改革；（新事物、思想或方法的）创造；新思想Evaluation 评价Dedicated 专注的；专用的Gratitude 感激之情；感谢Aeronautics 航空（学）的Astronautics 宇航The American Institute of Aeronautics and Astronautics (AIAA)Editor-in-Chief 主编总编辑Submit 提交呈送使服从使顺从derive from 起源于来自scope （题目、组织、活动等的）范围；能力perception 感知；知觉；看法；洞察力conviction 说服定罪确信信念observance 遵守(法律,规则,传统等)；(宗教的,正式的)仪式observed 观察；注意；看到；说vital 必不可少的；对…极重要的；生命的；维持生命所必需的violations 侵犯；违背；妨害；【体】违例Obligations义务；责任；债务；负担Authority 权威；权力；当局；授权Delegate n.代表；会议代表v.授（权）；把（工作、权力等）委托（给下级）；选派（某人做某事）Confer 协商；商讨；交换意见；授予（奖项、学位、荣誉或权利）Unbiased 公正的；不偏不倚的；无偏见的Impartial 公正的；不偏不倚的；中立的Merits n.优点价值功过功绩v.值得。
Predict and reduce gear whine noise 5 times faster Generate transmission gearbox models automatically and boost vibro-acoustic performanceUnrestricted© Siemens AG 2019Realize innovation.Transmission Engineering ChallengesGuarantee Performance and DurabilityReduce Time for SimulationMinimize Vibration and Noise LevelsReduce Weight with Lightweight DesignsAnalysisResultsModellingPrototyping can cost up to 200k$ --per single gear80% of time for manual model creationMicrogeometry modificationscan reduce vibration level with 6dB (=half!)Transmission Error can increase 10x or more!Transmission Engineering ProcessTypical process for NVH analysisMore efficient process in Simcenter 3DTransmission Error or Stiffness, parametersAcoustics, NVH •Gear whine •Gear rattleEnd-to-end integrated process for transmission simulation from CAD to Loads to NoiseTransmission Builder →Motion →Motion-to-Acoustics →Acoustic Analysis•Automatic creation of multi-body simulation models •Accurate 3D simulation of gear forces•Semi-automatic link of gear forces to vibro-acoustics •Efficient and accurate acoustic simulationsPre-processing of loads orsurface vibrationsTransmission layout (stages, dimensions)Multi-body simulation •Simulation of forcesand dynamicsPositioning, dimensions…Gear-centric tool•Analysis of gear pairsMulti-Body Simulation of TransmissionsTransmission Engineering ProcessTypical process for NVH analysisMore efficient process in Simcenter 3DTransmission Error or Stiffness, parametersAcoustics, NVH •Gear whine •Gear rattleEnd-to-end integrated process for transmission simulation from CAD to Loads to NoiseTransmission Builder →Motion →Motion-to-Acoustics →Acoustic Analysis•Automatic creation of multi-body simulation models •Accurate 3D simulation of gear forces•Semi-automatic link of gear forces to vibro-acoustics •Efficient and accurate acoustic simulationsPre-processing of loads orsurface vibrationsTransmission layout (stages, dimensions)Multi-body simulation •Simulation of forcesand dynamicsPositioning, dimensions…Gear-centric tool•Analysis of gear pairs.Transmission BuilderSummaryNew Simulation Solution for GearsMulti-Body Simulation of TransmissionsMulti-Body SimulationScopePredicting, Analyzing, Improving the positions, velocities, accelerations and loads of a mechatronic system using an accurate and robust 3D multi-body simulation approachMechatronic Systems Flexible Bodies•Integration with tools for robust design of complex non-linear multi-physics systems:control systems, sensors, electric motors, etc •Predict mechanical system more accurately wrt displacements and loads•Gain insight in frequency response of a mechanism•Enable Noise, Vibration & Harshness (NVH) as well as Durability analysesSimcenter 3D Motion for Transmission Simulation Critical featuresMulti-Body Simulation Industry Modelling Practices•Joints •Constraints •Bearings•Linear Flexible Bodies•Nonlinearity (geometric & materials) by running FEcode•Deformations•Loads•Transmission Error•Time domain •Statics, dynamic,•Mechatronics / controlPost processing•Create gear geometry ✓CAE interface ✓Import CAD•Ext. Forces •Motor•Contacts, FrictionParametric Optimization loop Automation / CustomizationKinematicsDynamicsFlexible bodiesCADSolving1D -modelsControlsTEST dataA manual creation process can consume 80%of time!.Transmission BuilderSummaryNew Simulation Solution for GearsMulti-Body Simulation of TransmissionsNew ApproachTransmission Builder Vertical ApplicationProblem: Even experienced 3D-Multi Body Simulation experts can struggle to 1.Model complex parametric transmissions2.Capture all relevant effects correctly and efficiently3.Update and validate their modelsSolution: Transmission Builder Up to 5x faster Model creation processSimcenter TransmissionBuilderGear train specification based on Industry standardsMultibody simulation modelDemonstrationModel Creation and Updating1.Loading of pre-definedTransmission2.Geometry creation3.Creation of rigid bodies forgearwheels and shafts4.Positioning and Joint-definition5.Force element creation.Transmission BuilderSummaryNew Simulation Solution for GearsMulti-Body Simulation of TransmissionsNew Solver Methodologies Simulating and ValidatingValidation cases ensure resultsas accurate as non-linear Finite Elements simulationMeasured Transmission ErrorAnalytical MethodSiemens STS Advanced MethodExploiting intrinsic geometric properties of gears + Efficient-Only for gears, not for arbitrary shapes-No deformation includedBut, included as part of the Load CalculationFE based contact detection -“Brute force” Slow+ Any geometry+ Deformation effects includedDedicating Tooth ContactModeling –FE PreprocessorLocal Deformation –Analytic SolutionSlicing –Gear Force Distribution Along Line of Action •Includes Microgeometry Modifications and Misalignments in all DOF•Automatically takes in to account coupling between slices and between teeth•Accounts for actual gear body geometry with advanced stiffness formulation•Evaluates tip contact (approximation)Gear ContactMethodology HighlightsKey Features.Transmission BuilderSummaryNew Simulation Solution for GearsMulti-Body Simulation of TransmissionsMulti-Body Simulation of Transmissions SummaryValidated methodologySuperior insight in transmission vibrationsAutomated creation of transmission modelsGear simulation as accurate as FE whileextremely fast•Create CAD + MBD model•Connect and position housing•Add flexible modes (Autoflex)•Set up load casesSimcenter 3D Motion Simulate TransmissionDynamic bearing forcesSimulateAcoustic Simulation of TransmissionsTransmission Engineering ProcessTypical process for NVH analysisMore efficient process in Simcenter 3DTransmission Error or Stiffness, parametersAcoustics, NVH •Gear whine •Gear rattleEnd-to-end integrated process for transmission simulation from CAD to Loads to NoiseTransmission Builder →Motion →Motion-to-Acoustics →Acoustic Analysis•Automatic creation of multi-body simulation models •Accurate 3D simulation of gear forces•Semi-automatic link of gear forces to vibro-acoustics •Efficient and accurate acoustic simulationsPre-processing of loads orsurface vibrationsTransmission layout (stages, dimensions)Multi-body simulation •Simulation of forcesand dynamicsPositioning, dimensions…Gear-centric tool•Analysis of gear pairs.Acoustic Simulation of TransmissionsAcoustic SimulationPost-ProcessingSummaryAcoustic Process OverviewvvcvMulti-body simulation resultsD a t a p r o c e s s i n g a n d m a p p i n gLoad Recipe Time series Frequency spectraWaterfalls OrdersNoise PredictionMeasured dataORAcoustic Process OverviewFrom Motion to AcousticsInput Loads Time Data to Waterfallof Time DataFFT Post-Processing•Multi-body simulation results•Data selection (forces, vibrations)•Automatic mapping •Multiple RPM•RPM function•Frame size definition•Time range selection•Time segmentation•Fourier transform(windowing, frequencyrange, averaging)•Waterfalls•Functions•Order-cut analysis Benefits•Quick switch between Motion and Acoustics solutions•Efficient data processing (fast pre-solver)•Automatic data mapping•Pre-processing time reductionAcoustic Process Overview Acoustic SimulationGeometry Preparation Meshing andAssemblyStructural/AcousticPre-ProcessingSolver Post-Processing•Holes closing •Blends removal •Parts assembly •Mesh mating•Bolt pre-stress•Structural meshing•Acoustic meshing•Loading frommulti-body analysis•Fluid-StructureInterface•Output requests•Simcenter NastranVibro-Acoustics(FEM AML,FEMAO, ATV)•Structural results•Acoustic results•Contributionanalysis (modes,panels, grids) What-If, Optimization, Feedback to DesignerBenefits•Efficient model set-up•Efficient, accurate solutions•Quick solution update•Deep insight into results.Acoustic Simulation of TransmissionsAcoustic SimulationPost-ProcessingSummaryAcoustic SimulationModel Preparation –MeshesFrom multi-body analysis•CAD geometry•Structural mesh of body→Used to compute structural modes included in Motion model when accounting for flexibility of body Specific to acoustic analysis•Acoustic mesh around body for exterior noise radiation →Geometry cleaning (ribs removal, holes filling)→Surface and convex meshing →3D elements filling•Microphone mesh for acoustic responseAssembly of structural and acoustic meshesBenefits•Easy, fast, efficient model set-up•Quick switch between CAD and FEM environments •Quick update with associativity of meshes to CAD •Flexible modelling through assemblyAssociativityModel Preparation –Loads and Boundary Conditions Structural constraints and loads•Fixed constraints•Multi-body forces applied at center of bearings→Automatic mapping→Data processing (time to waterfall of time data, FFT) Acoustic boundary conditions•AML (Automatically Matched Layer)→Non-reflecting boundary condition to absorb outgoing acoustic wavesFluid-structure interface•Weak or strong couplingTime dataTo Waterfall of Frequency dataBenefits•Easy, fast, efficient model set-up•Quick switch between FEM and SIM environmentsρc AMLSize ~ 190k nodes ~ 14k nodes Timex s/freq.x/20s/freq.AML (Automatically Matched Layer)•Automatic creation of PML (Perfectly Matched Layer) at solver levelFull absorption of outwards-traveling waves•First, accurate results in “physical” (red) FEM domain •Then, accurate results outside the FEM domain (green), through post-processing •PML layer very close to radiatorBenefits•No manual creation of extra absorbing layer •Optimal absorption •Lean FEM model •Fast computationSolver Technologies –FEM AMLATV (Acoustic Transfer Vector)•Single computation of acoustic transfer vector between vibrating surface and microphones{p ω}=ATV ω×{v n (ω)}•Independence of ATV from load conditions (RPM, order)•For exterior radiation, smooth ATV functions in frequencyBenefits•Large frequency steps for ATV computation, and interpolation for acoustic response •Fast multi-RPM analysisSolver Technologies –ATV=+p ωv n (ω)304050607080901001003005007009001100130015001700S o u n d P r e s s u r e L e v e l (d B )f (Hz)FEMATV Response Frequency100-1700 Hz 100-1700 HzTime22 min3 minNo ATV ATVFEMAO (FEM Adaptive Order)•High-order FEM with adaptive order refinement •Hierarchical high-order shape functions•Auto-adapting fluid element order at each frequency (dependent on f, local c0, local ℎ), to maintain accuracy Benefits•Lean single coarse acoustic mesh •Optimal model size at each frequency •Huge gains vs standard FEM •Faster at lower frequencies•More efficient at higher frequencies • 2 to 10 x fasterAcoustic SimulationSolver Technologies –FEMAOStandard FEM →1 single model for all frequenciesStandard FEM →several modelsfor different frequency rangesFEMAO →1 single model for all frequenciesLess DOF required forFEMAO Optimal DOF size over all frequenciesEdge Shape Functions Face Shape FunctionsFEM FEMAO.Acoustic Simulation of TransmissionsAcoustic SimulationPost-ProcessingSummaryRigid body vs Flexible body•No significant difference at low frequencies •Above 1400 Hz, more frequency content due to structural modes of flexible housing structurePlain gears vs Lightweight gears (flexible body)•Low harmonic at 200 Hz (6000 RPM), due to gear stiffness variation with holes in lightweight gear •Side band due to tooth stiffness variation (amplitude effect due to coupling with holes)Bearing Forces Frequency Domain Benefits•Deeper insight on input forces•Quick solution update for comparative studies involving design/modelling changesPlain gears vs Lightweight gears (flexible body)•Low RPM•Significant impact of lightweight gears •High RPM•Extra frequency content at low frequenciesRigid body vs Flexible body •Low frequencies•Reduced impact of flexibility •High frequencies•Larger impact of flexibilityRadiated Acoustic Power Functions300 RPM –Plain gears300 RPM –Lightweight gear 5900 RPM –Plain gears5900 RPM –Lightweight gears300 RPM –Rigid body 300 RPM –Flexible body 1500 RPM –Rigid body 1500 RPM –Flexible bodyBenefits•Efficient post-processing for results analysis •Quick solution update for comparative studiesinvolving design/modelling changesRigid Body vs Flexible Body Benefits•Efficient post-processing forresults analysis•Global overview oncorrespondencebetween source(dynamic forces)and receiver(acoustic power)Plain Gears vs Lightweight Gears Benefits•Efficient post-processing forresults analysis•Global overview oncorrespondencebetween source(dynamic forces)and receiver(acoustic power)Contribution AnalysisExamplesMultiple results types: structural displacements and modes, equivalent radiated power, acoustic pressure and power, panel contributions to pressure and power, grid contributions, etcBenefits•Efficient post-processing forresults analysis•Deepunderstanding ofmodel behaviorthrough multipleresults types Structural displacements Acoustic pressure Grid contributionsPanel contributions.Acoustic Simulation of TransmissionsAcoustic SimulationPost-ProcessingSummaryAcoustic Simulation of Transmissions SummaryEfficient model set-up with CAD associativity for quicksolution updateSuperior insight in vibro-acoustic responseFast and accurate solver technologiesMore efficient link of gear forces from Motion toAcoustics =+p ωv n (ω)Associativity•Transfer bearing forces into frequency domain•Set-up vibro-acoustic model•Map bearing forces onto vibro-acoustic modelSimcenter 3D Acoustics Simulate TransmissionSimulateAcoustic resultsConclusionUnrestricted © Siemens AG 20192019-05-08Page 42Siemens PLM SoftwarePredict and Reduce Gear Whine Noise 5 Times FasterGenerate transmission gearbox models automatically and boost vibro-acoustic performanceSimcenterTransmission Builder Motion Simulation Acoustic SimulationAutomation removes 80% of workload for transmission model generation New gear solver increases efficiencyand accuracy Automatic motion-to-acoustics linksimplifies pre-processing Fast acoustic solver gives superiorinsight to responseUnrestricted © Siemens AG 20192019-05-08Page 43Siemens PLM SoftwareEasy workflow from design specifications NVH gear whine analysisHyundai Motor CompanyGear Whine Analysis of Drivetrains Using Simcenter Simulation & Services•Predictive simulation for system level NVH and gear whine•Bring 3D simulation to the next level of usability, towards an holistic generative approach for drivetrain design and NVH“Simcenter Engineering and Consulting services helped us use the right analysistools to cover the entire gear transmission analysis […] The Simcenter 3D Transmission Builder software tool is well suited for our engineering purposes”Mr. Horim Yang, Senior Research Engineer•Simcenter 3D Motion and Transmission Builder for system level NVH in multibody •Simcenter Engineering and Consulting for solving complex engineering issues AutomaticCAD and multibody creationAccurateFE-based gear elementsMulti-disciplinaryCAD-FEMMultibody-Acoustichttps://youtu.be/bBM5TPP6iBg。
填空1.By dividing the force by the cross-sectional area, we can find the stress in the bar. And by dividing the elongation by the length along which the elongation occurs, we can find the strain in the bar.2.For the typical shape of the stress-strain diagram, the axial strains are plotted on the horizontal axis (abscissa) and the corresponding stresses are given by the ordinates.3.When the material begins to strain harden, it will offer additional resistance to increase in load.4.The presence of a pronounced yield point followed by large plastic strains is somewhat unique to steel. Aluminum alloys exhibit a more gradual transition from the linear to the nonlinear region.5.GJ is known as the torsional rigidity of the shaft.6.Let us consider a bar of circular cross section twisted by couples T acting at the ends. A bar loaded in this manner is said to be in pure torsion.7.It can be shown from considerations of symmetry that cross sections of the circular bar rotate as rigid bodies about the longitudinal axis, with radii remaining straight and the cross sections remaining circular.8.when a shaft is subjected to pure torsion, the rate of change of the angle of twist is constant along the length of the bar.9.J=∫ρ2dA is the polar moment of inertia of the circular cross section10.A bar that is subjected to forces acting transverse to its axis is called a beam.11.The beam, with a pin support at one end and a roller support at the other, is called a simply supported beam, or a simple beam.12.The beams that have a large number of reactions than the number of equations of static equilibrium are said to be statically indeterminate.13.The beam, which is built-in or fixed at one end and free at the other end, is called a cantilever beam.14.The axial force acting normal to the cross section and passing through the centroid of the cross section, shear force acting parallel to the cross section, and bending moment acting in the plane of the beam are known as stress resultants.15.One method for finding deflections of beams is the moment-area method. The name of this method comes from the fact that it utilizes the area of the bending moment diagram.16.It can be seen that the normal stress of a beam is a maximum at the outer edges and is zero at the neutral axis; the shear stress is zero at the outer edges and usually reaches a maximum at the neutral axis.17.The essential feature of a simple beam is that both ends of the beam may rotate freely during bending, but they cannot translate in the lateral direction18.When the beam is statically indeterminate, we cannot solve for the forces on the basis of statics alone. Instead, we must take into account the deflections of the beam and obtain equations of compatibility to supplement the equations of statics.19.Internal slots and holes of arbitrary shape can be modeled by ellipses with the same minimum radius of curvature and overall length.20.External notches can be modeled by hyperbolas with the same minimum radius of curvature.21.The irregularities in the body, such as holes, cracks, or notches, always induce an elastic stressnear the irregularity which may be considerably greater than the nominal stress calculated from the loads and the net cross sectional area of the body.22.The circular hole has a stress concentration factor of three in a uniaxial state of stress.23.If a column which is long compared to its width is subjected to axial force, it may fail by buckling, that is, the deflection increases rapidly as the load approaches a certain critical value. 24.The critical load can be increased by increasing the moment of inertia of its cross section. This result can be accomplished by distributing the material as far as possible from the centroid of the cross section.25.Tubular members are more economical for columns than are solid members having the same cross-sectional area.26.(Fill): The reference configuration is often taken as the shape of the unloaded structure.27.(Fill): For unstable structures, the potential energy may have either a maximum value or a neutral value.28.(Fill): A virtual displacement is an imaginary displacement. The work done by the real forces during a virtual displacement is called virtual work.29.(Fill): Materials can deform in many different ways. it can deform elastically, plastically, viscoelastically , or in a viscous manner.30.(Fill): Elastic deformation may be defined as a reversible deformation, i. e., after the applied load is removed, the body returns to its original shape and all stored energy can be recovered. 31.(Fill): Plastic deformation is a permanent deformation, i.e., after the applied load is removed, the body remains deformed and net work has been done.32.(Fill): The energy which must be supplied to propagate a brittle crack is usually less than the elastic strain energy released by the growth of the crack.判断1.(T/F): Brittle materials will undergo large strains before failure, ductile materials fail at relatively low values of strain2.(T/F): If the actual cross-sectional area at the narrow part of the neck is used in calculating , it will be found that the real stress never diminish.3.(T/F): Because of torsion, a rectangular element on the surface of the bar will be distorted into a rhomboid.4.(T/F): Equal shear stresses always exist on mutually parallel planes5..(T/F): If a material that is weaker in tension than in shear is twisted, failure occurs in tension along a helix inclined at 45°the axis.6.(T/F): The shear strain and shear stress vary linearly with the radial distance from the center of the shaft and have their minimum values at the outer surface.7.(T/F): The state of pure shear stress on the surface of the shaft is equivalent to equal tensile and compressive stresses on an element rotated through an angle of 45°to the axis of the shaft.8.(T/F): If a beam is acted upon by a concentrated force, there will be an abrupt changes, or discontinuity, in the bending moment diagram at the point of application of the concentrated force.9.(T/F): The solution for an elliptic hole can be used to obtain approximate stress concentration factors for other shapes of holes.10.(T/F): The potential energy method applies for any elastic structure, whether it behaves linearlyor nonlinearly.11.(T/F): The principle of virtual work applies to all structures irrespective of whether the material behaves linearly or nonlinearly, elastically or inelastically.12.The virtual change in shape must be compatible with the condition of the support for the structure and must maintain continuity between elements of the structure.13(T/F): In the applications normally encountered with metals, the normal stress does not significantly affect the sliding process, therefore, it may be stated that only the shear stress can be and does induce plastic deformation in metals.14.(T/F): Viscous material can be deformed substantially by a small load if the duration of loading is long.15.(T/F): Ductile fracture is preceded by considerable permanent change in the shape of the body. (T)16.(T/F): Ductile cracks are often able to grow at very high velocities, comparable to the speed of sound in the material. (F)17.(T/F): Fatigue fracture is often preceded by general plastic deformation of the body. (F)18.(T/F): Creep fracture is preceded by general permanent deformation of the body. (T)汉译英1.(C2E): 所有坐标系都是三维右手直角坐标系（笛卡尔坐标系）。
Journal of Sound and<ibration(2001)247(1),97}115doi:10.1006/jsvi.2001.3716,available online at onDYNAMIC STIFFNESS FORMULATION AND FREE VIBRATION ANALYSIS OF CENTRIFUGALLY STIFFENEDTIMOSHENKO BEAMSJ.R.B ANERJEEDepartment of Mechanical Engineering and Aeronautics,City;niversity,Northampton Square,¸ondon EC1<0HB,England.E-mail:j.r.banerjee@(Received24October2000,and in,nal form6March2001)The dynamic sti!ness matrix of a centrifugally sti!ened Timoshenko beam has been developed and used to carry out a free vibration analysis.The governing di!erential equations of motion of the beam in free vibration are derived using Hamilton's principle and include the e!ect of an arbitrary hub radius.For harmonic oscillation the derivation leads to two di!erent(but of similar form)fourth-order ordinary di!erential equations with variable coe$cients that govern the amplitudes of bending displacement and bending rotation respectively.An outboard force at the end of the beam is taken into account which makes possible the free vibration analysis of rotating non-uniform or tapered Timoshenko beams.Using the Frobenius method of series solution and imposing boundary conditions,the dynamic sti!ness matrix,which relates amplitudes of harmonically varying forces with the amplitudes of harmonically varying displacements at the ends of the element,is formulated.Applying the Wittrick}Williams algorithm to the resulting dynamic sti!ness matrix the natural frequencies of a few carefully chosen illustrative examples are obtained.The results are compared with those available in the literature. 2001Academic Press1.INTRODUCTIONThe free vibration analysis of a centrifugally sti!ened Bernoulli}Euler beam has been carried out by a number of investigators using di!erent methods[1}6].Recently, a contribution has been made to this literature by the present author who developed for the "rst time a dynamic sti!ness matrix to study the free vibration characteristics of rotating uniform and non-uniform Bernoulli}Euler beams[7].The superiority of the dynamic sti!ness method over"nite element and other approximate methods in predicting the natural frequencies and mode shapes of structures or structural elements accurately is well known[8}10].It is also commonly accepted that the Timoshenko beam theory,which accounts for the e!ects of shear deformation and rotatory inertia,is more accurate than the Bernoulli}Euler beam theory,particularly when the cross-sectional dimensions of the beam are relatively large,and when higher natural frequencies are required.Thus,the solution of the free vibration problems of rotating Timoshenko beams using the dynamic sti!ness method is a natural extension of the author's recent work[7].There are of course,a number of published papers on the subject of rotating Timoshenko beams[11}16]and on various similar aspects of non-rotating structures[17}22]using other methods.This new development of dynamic sti!ness theory is of considerable complexity,requiring substantial analytical and computational e!orts.The main focus of this research is to investigate the98J.R.BANERJEEfree vibration characteristics of rotating.Timoshenko beams by extending the elegantpower of the dynamic sti!ness method.This research is partly motivated by two recent papers[14,15]on the subject in which aninaccurate di!erential equation has unfortunately been used when solving the free vibrationproblem of rotating Timoshenko beams.In particular,a signi"cant term related to therotational speed was omitted in these papers by their authors while formulating thegoverning di!erential equations of motion for the problem and thus devaluing the theory.As a consequence the numerical results reported[14,15]are not su$ciently accurate(particularly for higher rotational speeds).This,of course,contradicts the claim made by theauthors of reference[15]that their theory provides a benchmark solution to the problem(see the last line of their conclusions).In the analysis presented below the inaccuracies ofreferences[14,15]are corrected and the problem is addressed in a judicious manner usinga new approach based on the dynamic sti!ness solution to the problem.The results from thepresent theory are contrasted with those reported in references[14,15].The investigation is carried out in the following steps.First,the governing di!erentialequations of motion of a rotating Timoshenko beam undergoing free natural vibration arederived using Hamilton's principle.Assuming harmonic oscillation the equations are thensolved using the Frobenius method of series solution.Next,the boundary conditions forbending displacements,bending rotation,shear force and bending moment are imposed andthe arbitrary constants are eliminated from the general solution.This essentially recasts theensuing equations in the form of a dynamic sti!ness matrix of a rotating Timoshenko beamelement,relating amplitudes of harmonically varying forces with amplitudes ofharmonically varying displacements at its ends.Finally,the resulting dynamic sti!nessmatrix is applied using the Wittrick}Williams algorithm[23]to obtain natural frequenciesof some carefully chosen examples.The results are compared with published results andsome conclusions are drawn.2.THEORYFigure1(a)shows in a rectangular Cartesian co-ordinate system,the notation used fora rotating Timoshenko beam which has four uniform parts AB,BC,CD and DE,respectively,with each having uniform properties so that the assembly forms a steppedbeam.The hub radius and the rotational speed are taken to be r&and ,respectively,as shown.A typical element BC(shown by the solid line in Figure1(a))which forms a part ofthe whole assembly is shown separately in Figure1(b).This element will be considered herein the dynamic sti!ness analysis.It is essential that the dynamic sti!ness matrix to bederived can be assembled for a number of such elements to form the dynamic sti!nessmatrix of the complete structure.This enables free vibration analysis of rotating tapered ornon-uniform Timoshenko beams.The origin of the element(see Figure1(b))is taken at theleft-hand end and is at a distance r G from the axis of rotation.The>-axis is considered to be coincident with the centroidal axis of the beam whereas the Z-axis is parallel,but not coincidental with the axis of rotation of the beam.(Due to the choice of right-handed co-ordinate system,the X-axis is perpendicular and away from the plane of the paper.)The total length of the stepped beam in Figure1(a)is¸2whereas the length of the typical element BC in Figure1(b)is¸.An outboard force F at the right-hand end of the element BC that may arise as a result of the adjacent elements CD and DE is taken into account when developing the theory.Clearly,for the element DE,this force is zero.Attention is here con"ned to the derivation of the dynamic sti!ness matrix correspondingto the out-of-plane vibration of the beam in the>Z-plane only.The corresponding dynamicFigure 1.(a)Co-ordinate system and notation for a rotating Timoshenko beam formed by four uniform elements so as to form a stepped beam of length ¸2;(b)Co-ordinate system and notation for a rotating Timoshekno beam element of length ¸.sti !ness matrix related to the in-plane vibration in the X >-plane of the beam can be derived by following the same procedure and by suitable substitution of beam parameters [4,7].The two governing partial di !erential equations of motion for free vibration in the >Z -plane of the Timoshenko beam BC are derived using Hamilton 's principle (see Appendix A for details).They are(¹w ) ! Aw #kAG (w ! )"0,EI #kAG (w ! )! I # I "0,(1,2)where ¹,the centrifugal tension at a distance y from the origin,is given by [7]¹(y )" A [r G ¸# ¸ !r G y !y ]#F ,(3)EI and kAG are,respectively,the bending the shear rigidity, is the density of the material,A is the area of cross-section (so that A is the mass per unit length),I is the second moment of area of the beam cross-section about the X -axis.A prime and an over dot denote di !erentiation with respect to distance y and time t respectively.Equations (1)and (2)de "ne completely the free vibration characteristics of a uniform rotating Timoshenko beam.Note that the term I in equation (2)which can be CENTRIFUGALLY STIFFENED TIMOSHENKO BEAMS 99signi "cant for higher rotational speed ,is omitted by the authors of references [14,15].The physical origin of this term lies in the fact that the centrifugal force on elements symmetrically placed with respect to the mid-plane of the beam cross-section have di !erent radii from the axis of rotation when undergoing bending deformation,and so have di !erent centrifugal forces.This generates a moment which is I .(The corresponding net centrifugal force is independent of section rotation.)For harmonic oscillation the term I indicates an increase in rotatory inertia of the element,see equation (2).Assuming simple harmonic oscillation,w and can be written asw (y ,t )"=(y )e i t , (y ,t )" (y )e i t .(4)Substituting equation (4)into equations (1)and (2)and introducing the non-dimensional parameter"y /¸(5)it can be shown,after considerable algebraic manipulation,that equations (1)and (2)with the help of equation (4)can be expressed as two di !erent,but similar,fourth order ordinary di !erential equations with variable coe $cients as follows.(Note that for a centrifugally sti !ened Bernoulli }Euler beam the formulation leads to only one di !erential equation which applies to both the bending displacement and the bending rotation [7].)(C #C #C )d =d#(C #C )d =d #(C #C #C )d =d #(C #C )d =d #C="0,(6)(C* #C* #C* )d d #(C* #C* )d d #(C* #C* #C* )d d#(C* #C* )d d #C*"0,(7)whereC "1# s ( # )#p s ,C* "C:C "! s ,C* "C ,(8,9)C "! s ,C* "C :C "!3 s ,C* "2C :C "!3 s ,C* "4C,(10}12)C " ( # )#(r #s )( # )#p !4 s ,C * "C !4C,(13)C "! ,C* "C :C "! ,C* "C :C "C ,C* "2C.(14}16)C "2C ,C* "4C :C " ,C* "C #2C(17,18)withr "I A ¸ ,s "EI kAG ¸ ,p "F ¸ EI , "y ¸, "r &¸, " A EI ¸ , " A ¸ EI(19)and"r s ( # )!1.(20)100J.R.BANERJEEThe di!erential equations(6)and(7)are of the same form and are amenable to power seriessolution in terms of the independent variable .Note that for a non-rotating Timoshenkobeam( "0)the two di!erential equations become identical which accords with theformulation given by Howson and Williams[24].The solutions of the di!erential equations(6)and(7)will be of the same form provided the constants C }C and C* }C* are interpreted ing the method of Frobenius,the solution is sought in the form ofthe following series[4,7,15]:>(c, )"La L> (c) A>L,(21)where a L> are the coe$cients and c is an undetermined exponent.Substituting equation (21)into equation(6)or(7),one obtains the following indicial equation[4,7,15]:c(c!1)(c!2)(c!3)"0,(22) and the following recurrence relationship:a L> (c)"!a L> (c)C (c#n)#CC (c#n#4)!aL> (c)C (c#n)(c#n!1)#C (c#n)#CC (c#n#4)(c#n#3)!aL> (c)C (c#n)#CC (c#n#4)(c#n#3)(c#n#2)!aL> (c)C (c#n)(c#n!1)#C (c#n)#CC (c#n#4)(c#n#3)(c#n#2)(c#n#1),n*0(23)where the"rst four coe$cients can be de"ned with the help of equations(6)(or(7))and(21) as follows.(Note that this formulation is similar to,but di!erent from that of reference[15] because in equation(21), A>L,instead of L,has been used.)a (0)"1,a (0)"0,a (0)"0,a (0)"0.(24)a (1)"1,a (1)"0,a (1)"0,a (1)"!C /(24C ),(25)a (2)"1,a (2)"0,a (2)"!C /(12C ),a (2)"+C (C #C )!C (C #C ),/(60C ),(26)a (3)"1,a (3)"!C /(4C ),a (3)"+C (C #C )!C (C #C ),/(20C ),a (3)"![(2C #C )+C (C #C )!C (C #C ),!C C (2C #2C #C )#C(2C #C )]/(120C ).(27) Equations(23)}(27)apply for the solution of=,but they can also be applied for the solution of provided that C }C are replaced by C* !C* .(In order to avoid confusion on asterisk has been introduced to designate the terms as a*L> to be used for the solutions of .) The roots of the indicial equation(22)are c"0,1,2,3so that the solutions for=and of each of equations(6)and(7)can be expressed as linear combinations of four independent solutions as=( )"A>(0, )#A >(1, )#A >(2, )#A >(3, ),(28) ( )"B (0, )#B (1, )#B (2, )#B (3, ),(29)CENTRIFUGALLY STIFFENED TIMOSHENKO BEAMS101where A }A and B }Bare two di !erent sets of constants and >(0, )"1#a (0) #a (0) #2,>(1, )" #a (1) #a(1) #2,(30,31)>(2, )" #a (2) #a (2) #2,>(3, )" #a (3) #a (3) #2,(32,33) (0, )"1#a* (0) #a* (0) #2, (1, )" #a* (1) #a*(1) #2,(34,35) (2, )" #a* (2) #a* (2) #2, (3, )" #a* (3) #a*(3) #2.(36,37)It can be shown with the help of equation (6)or (7)that the constants of A }A and B }B used in the solutions for =and ,see equations (28)and (29),are related as follows:0100002000034a (0)4a (1)4a (2)4a (3) A /¸A /¸A /¸A/¸"!s /s 0200 /s 0612a * (0)12a * (1)12a * (2)# /s 12a * (3)20a * (0)20a * (1)20a * (2)20a * (3)# /s B B B B.(38)The 4;4square matrix on the right side was pre-multiplied by the inverse of the 4;4square matrix of the left side to obtain explicit expressions for the A /¸,A /¸,A /¸and A /¸.This was achieved by making extensive use of symbolic computation [25,26]which was essentially desirable because the terms a (0),a (1),a (2),a (3),etc.,are algebraic expressions and not numbers.In this way A }A are related to B }Bas follows:A /¸"R B #R B #R B #R B ,A /¸"R B #R B,(39)A /¸"R B #R B ,A /¸"R B #R B #R B #R B,(40)whereR "C / ,R "(!s #C !3s C )/( ),R "2(!3s C #s C #3C)/( ),(41)R "6C / ,R "! ,R "!2s ,R "! /2,R"!3s ,R "s ( #C )/(6C),(42,43)R "s C /3C ,R "(!4s C #s C !C )/(3C ),R "2s C /C.(44)Using the sign convention of Figure 2and noting that a prime now denotes di !erentiation with respect to ,the expressions for bending moment M ( )and shear force Q ( )can be written as (see Appendix A)M ( )"!(EI /¸)(d /d )"!(EI /¸)[ (0, )B # (1, )B # (2, )B # (3, )B]"!(EI /¸ )[ (0, )B ¸# (1, )B ¸# (2, )B ¸# (3, )B¸](45)102J.R.BANERJEEFigure 2.Sign convention for positive shear force (Q )and bending moment (M ).andQ ( )"!(1/¸)d M /d # I ( # )!(¹/¸)d =/d"(EI /¸ )[ ( )B # ( )B # ( )B # ( )B]"(EI /¸ )[ ( )B ¸# ( )B ¸# ( )B ¸# ( )B¸],(46)where( )" (0, )# (0, )!R g ( )> (0, )!R g ( )> (1, )!Rg ( )> (3, ),(47) ( )" (1, )# (1, )!R g ( )> (0, )!R g ( )> (2, )!Rg ( )> (3, ),(48) ( )" (2, )# (2, )!R g ( )> (0, )!R g ( )> (1, )!Rg ( )> (3, ),(49) ( )" (3, )# (3, )!R g ( )> (0, )!R g ( )> (2, )!Rg ( )> (3, ),(50)with"r ( # )(51)andg ( )"(1#2 !2 ! )#p .(52)In order to develop the dynamic sti !ness matrix of the rotating Timoshenko beam element the boundary conditions for displacement and forces are imposed.The end conditions for displacements and forces of the element (see Figure 3)are,respectively,given below.Displacements :at "0:=" ,and ";at "1:=" ,and " .(53,54)Forces :at "0:Q "Q ,and M "M ;at "1:Q "!Q ,and M "!M .(55,56)CENTRIFUGALLY STIFFENED TIMOSHENKO BEAMS 103Figure3.Boundary conditions for(a)displacements and(b)forces of the rotating Timoshenko beam. Substituting equations(53)and(54)into equations(28)and(29)and equations(55)and(56)into equations(45)and(46)and making use of equations(39,40)and(47)}(52)give "A "R (B ¸)#R (B ¸)#R (B ¸)#R (B ¸), "B ,(57,58) "S (B ¸)#S (B ¸)#S (B ¸)#S (B ¸),(59) "B (0,1)#B (1,1)#B (2,1)#B (3,1)(60) andQ "= [ (0)B ¸# (0)B ¸# (0)B ¸# (0)B ¸],M "!= (B ¸),(61,62) Q "!= [ (1)B ¸# (1)B ¸# (1)B ¸# (1)B ¸],(63) M "= [ (0,1)B ¸# (1,1)B ¸# (2,1)B ¸# (3,1)B ¸],(64) whereS "R >(0,1)#R >(1,1)#R >(3,1),S "R >(0,1)#R >(2,1)#R >(3,1),(65,66) S "R >(0,1)#R >(1,1)#R >(3,1),S "R >(0,1)#R >(2,1)#R >(3,1),(67,68) and= "EI/¸,= "EI/¸ ,= "EI/¸ (69) Equations(57)}(60)and(61)}(64)can be written in the following matrix form:" R ¸R ¸R ¸R ¸1000S ¸S ¸S ¸S ¸ (0,1) (1,1) (2,1) (3,1) BBBB (70)or"GB(71) 104J.R.BANERJEEandQ M Q M " = (0)= (0)= (0)= (0)0!= 00!=(1)!= (1)!= (1)!= (1)=(0,1)= (1,1)= (2,1)= (3,1) BBB B (72)orF"HB.(73) The dynamic sti!ness matrix K can be obtained by eliminating the constant vector B from equations(71)and(73)to give the force}displacement relationship asF"K (74) orQ M Q M " k k k k k k ksymmetric k kk,(75)whereK"HG\ (76) is the required dynamic sti!ness matrix.Each individual element of the matrix K is generated algebraically by inverting the G matrix and premultiplying the resulting matrix by the H matrix.This procedure was greatly assisted by the symbolic computing package REDUCE[25,26].The ten independent terms of the K matrix are obtained ask "= / ,k "k "= / ,k "k "= / ,k "k "= / ,(77}80) k "= / ,k "k "= / ,k "k "= / ,(81}83)k "= / ,k "k "= / ,k "= / ,(84}86) where"[S (0)!S (0)] (2,1)![S (0)!S (0)] (3,1)![S (0)!S (0)] (1,1),(87)"![S (3,1)!S (2,1)].(88) "[R (0)!R (0)] (2,1)#[R (0)!R (0)] (3,1)#[R (0)!R (0)] (1,1),(89)"[R S !R S ] (0)#[R S !R S ] (0)#[R S !R S ] (0),(90) "[R S !R S ] (3,1)#[R S !R S ] (0,1)#[R S !R S ] (2,1),(91) CENTRIFUGALLY STIFFENED TIMOSHENKO BEAMS105106J.R.BANERJEE"[R (3,1)!R (2,1)], "![R S !R S ],(92,93) "[R (1)!R (1)] (2,1)#[R (1)!R (1)] (1,1)#[R (1)!R (1)] (3,1),(94)"!R [ (2,1) (3,1)! (3,1) (2,1)]!R [ (3,1) (1,1)! (1,1) (3,1)]!R[ (1,1) (2,1)! (2,1) (1,1)],(95) "[R S !R S ] (3,1)#[R S !R S ] (2,1)#[R S !R S ] (1,1),(96) and"[R S !R S ] (1,1)#[R S !R S ] (2,1)#[R S !R S ] (3,1).(97) The above dynamic sti!ness matrix relates to the out-of-plane motion of the beam,in the >Z-plane of Figure1.The dynamic sti!ness matrix for the in-plane motion(in XZ-plane can be derived in a similar manner by suitable choice of parameters[4,7].2.1.APPLICATION OF THE DYNAMIC STIFFNESS MATRIXThe resultant dynamic sti!ness matrix can now be used to compute the natural frequencies and mode shapes of a rotating Timoshenko beam with various end conditions.A rotating non-uniform Timoshenko beam,for example a tapered Timoshenko beam,can also be analyzed for its free vibration characteristics by idealizing it as an assemblage of many uniform beams,and is thus treated as a stepped beam(see Figure1).An accurate and reliable method of calculating the natural frequencies and mode shapes is to use the dynamic sti!ness matrix method coupled with the well-known algorithm of Wittrick and Williams[23],which has featured in numerous papers.The algorithm,unlike its proof,is very simple to use[8}10],but for a detailed insight interested readers are referred to the original work of Wittrick and Williams[23].Basically,the algorithm needs the dynamic sti!ness matrices of individual members in a structure and information about their natural frequencies when both ends are clamped.This information is needed to ensure that no natural frequencies of the structure are missed.Thus an explicit expression from which the clamped}clamped natural frequencies can be found facilitates a straightforward application of the algorithm. in equation(97)is such an expression because the clamped}clamped natural frequencies are given by its zeros.It should be noted that the actual requirement of the algorithm is to isolate these clamped}clamped natural frequencies(that is to determine how many such natural frequencies are there below a speci"ed trial frequency)rather than actually calculating them.The Wittrick}Williams algorithm[8}10]essentially gives the number of natural frequencies of a structure that exists below an arbitrarily chosen trial frequency rather than actually calculating the natural frequencies.This simple feature of the algorithm can be used to calculate any natural frequency of the structure to any desirable accuracy.3.RESULTS AND DISCUSSIONUsing the above theory,the natural frequencies of rotating Timoshenko beams with cantilever end conditions were obtained for a range of illustrative examples.The results areT ABLE 1Fundamental natural frequency of a rotating ¹imoshenko beam with cantilever end condition for various values of the rotational speed parameter ,with r &"0,S R "30(r "1/30)and E /kG "3)059Fundamental natural frequency ( )Present theory Reference [14]Error (%)03)47983)4798013)64453)64520)01924)09714)09940)05634)75164)75580)08845)53145)53750)11056)38586)39340)119R The variable S (instead of r )where S "1/r is used here for a direct comparison of results with reference [14].presented in non-dimensional form and can be reproduced by using any set of appropriate data.However,it is instructive to use representative values for k ,E /G ,r and s (see equations(19))so that any possibility of numerical ill conditioning (as a result of using unrealistic values)can be avoided.During the current investigation typical numerical values used for k ,E /G ,r and s and 2/3,8/3,0)04and 0)08respectively.(Note that it can be shown with the help of equation (19)that for k "2/3and E /G "8/3,s "2r .)It was found that the convergence of the series solution was excellent.From a computational point of view,a total of 120terms was found to be completely adequate in obtaining results with su $cient accuracy.References [14,15],which give natural frequencies of rotating Timoshenko beams with cantilever end condition,were used and a direct comparison of results was made.The authors of reference [14]gave results using the transfer matrix method,but these were reported only for the fundamental natural frequency of the beam.Nevertheless,these results (see their Tables 3and 4)are reconstructed using the present theory.Tables 1and 2show results using the present theory and those reported in reference [14]using the transfer matrix method.(Note that the symbol S used in reference [14]is equal to 1/r for the present paper.)The results of Table 1illustrate the e !ect of the rotational speed parameter ( )on the fundamental natural frequency of the Timoshenko beam,and as expected,when "0complete agreement between the two sets of results is evident.However,the disagreement between the two sets of results increases with increasing rotational speed,and the reason for this is,of course,the fact that the authors of reference [14]omitted the term I in their formulation (see equation (2)).The e !ect of the Timoshenko beam parameter r ("1/S )on the fundamental natural frequency of the beam is shown in Table 2when the rotational speed parameter is set to 0and 5respectively.Here again the results from the present theory match exactly with those of reference [14]for the case when "0(except $1in the last digit for a few cases,which the author believes is a rounding error in reference [14]).Clearly,the results do not match for the case when "5because of the above reason.With increasing S (and hence decreasing r )the di !erence in results diminishes,as expected.Next,the illustrative examples of reference [15]are used for comparison.Unfortunately,the authors of reference [15]have given only one set of tabulated (numerical )results (see their Table 7)and they are only for the fundamental natural frequency of the rotating Timoshenko beam.In contrast,they have given a set of six tabulated (numerical )results for the "rst three natural frequencies of the corresponding Bernoulli }Euler beamT ABLE2Fundamental natural frequency of a rotating¹imoshenko beam with cantilever end condition for various values of S(S"1/r),when "0and "5with r&"0and E/kG"3)059 S( "0)( "5)Present theory Reference[14]Present theory Reference[14]203)43643)43646)31266)3241 303)47983)47986)38586)3934 403)49553)49546)41316)4179 503)50283)50286)42606)4294 803)51083)51086)44036)4418 1003)51273)51266)44366)4446 1503)51453)51446)44696)4476 2003)51523)51526)44816)4485 3003)51563)51556)44896)4493T ABLE3Fundamental natural frequency of a rotating¹imoshenko beam with cantilever end condition for various values of r and ,with r&"0,k"2/3,E/G"8/3.(¹he results shown inparentheses are from reference[15].)Fundamental natural frequency()r "0 "4 "8 "1203)51605)58509)256813)170(3)516)(5)585)(9)257)(13)170)0)013)51195)57919)244713)148(3)512)(5)580)(9)246)(13)150)0)023)49985)56169)209613)087(3)500)(5)564)(9)215)(13)095)0)033)47995)53329)154912)998(3)480)(5)539)(9)167)(13)015)0)043)45275)49519)085412)893(3)453)(5)505)(9)106)(12)923)0)053)41875)44879)006012)783(3)419)(5)463)(9)036)12)827)0)063)37875)39548)920812)672(3)379)(5)415)(8)963)(12)734)0)073)33355)33708)833312)564(3)333)(5)363)(8)889)(12)646)0)083)28375)27498)745612)458(3)248)R(5)307)(8)815)(12)564)0)093)23025)21048)658812)353(3)230)(5)249)(8)744)(12)487)0)13)17385)14488)573512)247(3)174)(5)191)(8)677)(12)415)R This"gure is taken from reference[15]and is probably in error.It could be a typographical error and the intended value is probably3)284instead of3)248.Figure4.The"rst three natural frequencies of a rotating Timoshenko beam for the case when "4( corresponds to the natural frequencies of Bernoulli}Euler beam).(see Tables1}6,pp.511}516of reference[15])which are actually peripheral to the main investigation.Nevertheless,the results obtained from the present theory are compared with those limited results given in reference[15].These are shown in Table3along with the results of reference[15]shown in parentheses.A complete agreement was expected because the present theory as well as the theory presented in reference[15]are both based on the solution of the governing di!erential equations,and therefore,both theories are expected to give exact results.This was not to be the case except when "0.As can be seen from the results of Table3,the discrepancy between the two sets of results increases with increasing values of the rotational speed( ).The reason for this,is again because of the omission of the term I in equation(2),by the authors of reference[15](see their equation(10)). The authors of reference[15]have given some graphical results,showing the variation of the"rst three natural frequencies of the cantilever Timoshenko beam with the parameter r, for three di!erent values of the rotational speed parameter (see Figures5}7of their paper). Using the present theory,one set of these results,which corresponds to the case "4,is shown in Figure4for comparison.A resemblance between this"gure and Figure5of reference[15]seems apparent.However,when examined and inspected closely by computed results,the discrepancy between the two"gures becomes noticeable.Figure5 shows the di!erence in the fundamental natural frequency of the rotating Timoshenko beam when using reference[15]and the present theory.For completeness,two additional sets of results were obtained.Figure6shows the"rst set in which the e!ect of rotational speed( )on the"rst three natural frequencies of the cantilever Timoshenko beam is demonstrated when r"0)04.The natural frequencies, which are non-dimensionalized with respect to the non-rotating case,increase with increasing because of the centrifugal sti!ening e!ect.As expected,the e!ect is relatively more pronounced for lower order frequencies than the higher order ones.The"nal set of results was obtained to assess the errors incurred,as a result of using the Bernoulli}Euler theory,as opposed to Timoshenko theory for the rotating beam.To this end the variation of the percentage error in the third natural frequency with rotational speed( )is shown in Figure7for three di!erent values of r.The error diminishes with rotational speed.This isexpected because at higher rotational speed the centrifugal sti!ness term dominates the。
