简介:从考虑损伤的粘弹性材料的一种卷积型本构关系出发,建立了在有限变形下损伤粘弹性Timoshenko梁的控制方程.利用Galerkin方法对该组方程进行简化,得到一组非线性积分-常微分方程.然后应用非线性动力学数值分析方法,如相平面图,Poincare截面分析了载荷参数对非线性损伤粘弹性Timoshenko梁动力学性能的影响.特别考察了损伤对粘弹性梁的动力学行为的影响.
简介:Inthispaper,theboundarystabiligstionoftbeTimoshenkoequationofanononiformbeam,withclarrmpedboundaryconditionatoneendandwitbbendingmomentandshearforcecontrolsattheotherend,isconsidered.Itisprovedthatthesystemisexponentiallystahilizablewhenthebendingmomentandshearforcecontrolsaresimultaneouslyappiied.Thefrequencydomainmethodandthemultipliertechniqueareused.
简介:Inthispaper,thestabilizationproblemofnonuniformTimoshenkobeambysomenonlinearboundaryfeedbackcontrolsisconsidered.Byvirtueofnonlinearsemigrouptheory,energy-perturbedapproachandexponentialmultipliermethod,itisshownthatthevibrationofthebeamundertheproposedcontrolactiondecaysexponentiallyorinnegativepoweroftimetast→∞.
简介:TheboundarystabilizationproblemofaTimoshenkobeamattachedwithamassatoneendisstudied.First,withlinearboundaryforcefeedbackandmomentcontrolsimultaneouslyattheendattachedwiththeload,theenergycorrespondingtotheclosedloopsystemisproventobeexponentiallyconvergenttozeroastimet--oo.Then,somecounterexamplesaregiventoshowthat,inothercases,thecorrespondingclosedloopsystemis,ingeneral,notstableasymtotically,letaloneexponentially.
简介:ThefeedbackstabilizationproblemofanonuniformTimoshenkobeamsystemwithrotorinertiaatthetipofthebeamisstudied.First,asaspecialkindoflinearboundaryforcefeedbackandmomentcontrolisappliedtothebeam'stip,thestrictmathematicaltreatment,asuitablestateHilbertspaceischosen,andthewell-posenessofthecorrespondingclosedloopsystemisprovedbyusingthesemigrouptheoryofboundedlinearoperators.Thentheenergycorrespondingtotheclosedloopsystemisshowntobeexponentiallystable.Finally,inthespecialcaseofuniformbeam,somesufficientandnecessaryconditionsforthecorrespondingclosedloopsystemtobeasymptoticallystablearederived.
简介:ThestabilizationoftheTimoshenkoequationofanonuniformbeamwithlocallydistributedfeedbacksisconsidered.Itisprovedthatthesystemisexponentiallystabilizable.Thefrequencydomainmethodandthemultipliertechniqueareapplied.
简介:Inthispaper,afiniteelementmethodisdevelopedtonumericallyevaluatetheshearcoefficientofTimoshenko'sbeamwithmultiplyconneetedcrosssection.Withfocusonanalyzingshearstressesdistributedattheneutralaxisofthebeam,animproveddefinitionoftheshearcoefficientispresented.Basedonthisdefinition,aGalerkin-typefiniteelementformulationisproposedtoanalyzetheshearstressesandsheardeflections.Numericalsolutionsoftheexamplesforsometypicalcross-sectionsarecomparedwiththetheoreticalresults.TheshearcoefficientoftowersectionsoftheTsingMaBridgeiscalculatedbyuseoftheproposedapproach,sothatthefiniteelementmodelingofthebridgecanbedevelopedwiththeaccuratevaluesofthesectionalproperties.