简介：摘要：粘弹性Timoshenko梁是一种结合了粘弹性和Timoshenko梁理论的新型工程力学理论，其发展具有重要的工程实践意义。本文将从概念、发展历程、应用前景等多个方面，全面介绍粘弹性Timoshenko梁的发展。

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：采用Timoshenko梁修正理论研究了有梯度界面层双材料梁的振动问题,利用静力方程确定了有梯度界面层双材料梁的中性轴位置,在此基础上应用Timoshenko梁修正理论建立了有梯度界面层双材料梁的振动方程,求得其自振频率表达式及其在简谐荷载作用下强迫振动的解析解.讨论分析了梯度界面层高度等因素对有梯度界面层双材料梁的振动影响,并用有限元法验证了Timoshenko梁修正理论.通过实例计算,得到了梯度界面层高度等因素对有梯度界面层双材料梁振动特性有较大影响的结论.

简介：OfconcernisaviscoelasticbeammodelledusingtheTimoshenkotheory.Itiswell-knownthatthesystemisexponentiallystableifthekernelinthememorytermissub-exponential.Thatis,iftheproductofthekernelwithanexponentialfunctionisasummablefunction.Inthisarticleweaddressthequestions:Whatifthekernelistestedagainstadifferentfunction(sayGamma)otherthantheexponentialfunction?Wouldtherestillbestability?Intheaffirmative,whatkindofdecayrateweget?Itisprovedthatforanon-decreasingfunction'Gamma'whose'logarithmicderivative'isdecreasingtozerowehaveadecayoforderGammatosomepowerandinthecaseitdecreasestoadifferentvaluethanzerothenthedecayisexponential.

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：ComplexmodesandtravelingwavesinaxiallymovingTimoshenkobeamsarestudied.Duetotheaxiallymovingvelocity,complexmodesemergeinsteadofrealvaluemodes.Correspondingly,travelingwavesarepresentfortheaxiallymovingmaterialwhilestandingwavesdominateinthetraditionalstaticstructures.Theanalyticalresultsobtainedinthisstudyareverifiedwithanumericaldifferentialquadraturemethod.

简介：Inthispaper,thenumericalapproximationofaTimoshenkobeamwithbound-aryfeedbackisconsidered.Wederivedalinearizedthree-leveldifferenceschemeonuniformmeshesbythemethodofreductionoforderforaTimoshenkobeamwithboundaryfeedback.Itisprovedthattheschemeisuniquelysolvable,unconditionallystableandsecondorderconvergentinL_∞normbyusingthediscreteenergymethod.Anumericalexampleispresentedtoverifythetheoreticalresults.

简介：在这份报纸，我们与线性摩擦抑制和对排水量方程起作用的分布式的延期考虑一个维的Timoshenko系统。在延期和波浪速度的重量上的合适的假设下面，我们建立通过摩擦抑制的驱散是足够强壮的一致地甚至面对延期稳定系统的系统和表演的well-posedness。

简介：ThepresentpaperinvestigatesthedynamicresponseoffiniteTimoshenkobeamsrestingonasixparameterfoundationsubjectedtoamovingload.ItisforthefirsttimethattheGalerkinmethodanditsconvergencearestudiedfortheresponseofaTimoshenkobeamsupportedbyanonlinearfoundation.ThenonlinearPasternakfoundationisassumedtobecubic.Therefore,theefectsofthesheardeformablebeamsandthesheardeformationoffoundationsareconsideredatthesametime.TheGalerkinmethodisutilizedfordiscretizingthenonlinearpartialdifferentialgoverningequationsoftheforcedvibration.ThedynamicresponsesofTimoshenkobeamsaredeterminedviathefourth-orderRunge–Kuttamethod.Moreover,theefectsofdiferenttruncationtermsonthedynamicresponsesofaTimoshenkobeamrestingonacomplexfoundationarediscussed.ThenumericalinvestigationsshowsthatthedynamicresponseofTimoshenkobeamssupportedbyelasticfoundationsneedssuperhigh-ordermodes.Furthermore,thesystemparametersarecomparedtodeterminethedependenceoftheconvergencesoftheGalerkinmethod.

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简介：Inthispaper,afiniteelementmethodisdevelopedtonumericallyevaluatetheshearcoefficientofTimoshenko'sbeamwithmultiplyconneetedcrosssection.Withfocusonanalyzingshearstressesdistributedattheneutralaxisofthebeam,animproveddefinitionoftheshearcoefficientispresented.Basedonthisdefinition,aGalerkin-typefiniteelementformulationisproposedtoanalyzetheshearstressesandsheardeflections.Numericalsolutionsoftheexamplesforsometypicalcross-sectionsarecomparedwiththetheoreticalresults.TheshearcoefficientoftowersectionsoftheTsingMaBridgeiscalculatedbyuseoftheproposedapproach,sothatthefiniteelementmodelingofthebridgecanbedevelopedwiththeaccuratevaluesofthesectionalproperties.

简介：Thebendingresponsesoffunctionallygraded(FG)nanobeamswithsimplysupportededgesareinvestigatedbasedonTimoshenkobeamtheoryinthisarticle.TheGurtin-MurdochsurfaceelasticitytheoryisadoptedtoanalyzetheinfluencesofsurfacestressonbendingresponseofFGnanobeam.ThematerialpropertiesareassumedtovaryalongthethicknessofFGnanobeaminpowerlaw.Thebendinggoverningequationsarederivedbyusingtheminimumtotalpotentialenergyprincipleandexplicitformulasarederivedforrotationangleanddeflectionofnanobeamswithsurfaceeffects.IllustrativeexamplesareimplementedtogivethebendingdeformationofFGnanobeam.Theinfluencesoftheaspectratio,gradientindex,andsurfacestressondimensionlessdeflectionarediscussedindetail.

简介：Inthispaper,aboundaryfeedbacksystemofaclassofnon-uniformundampedTimoshenkobeamwithbothendsfreeisconsidered.Alinearizedthree-leveldifferenceschemefortheTimoshenkobeamequationsisderivedbythemethodofreductionoforderonuniformmeshes.Theuniquesolvability,unconditionalstabilityandconvergenceofthedifferenceschemeareprovedbythediscreteenergymethod.Theconvergenceorderinmaximumnormisofordertwoinbothspaceandtime.Thevalidityofthistheoreticalanalysisisverifiedexperimentally.

简介：Thispaperdealswiththefreevibrationanalysisofcircularalumina(Al2O3)nanobeamsinthepresenceofsurfaceandthermaleffectsrestingonaPasternakfoundation.ThesystemofmotionequationsisderivedusingHamilton'sprincipleundertheassumptionsoftheclassicalTimoshenkobeamtheory.Theeffectsofthetransversesheardeformationandrotaryinertiaarealsoconsideredwithintheframeworkofthementionedtheory.Theseparationofvariablesapproachisemployedtodiscretizethegoverningequationswhicharethensolvedbyananalyticalmethodtoobtainthenaturalfrequenciesofthealuminananobeams.TheresultsshowthatthesurfaceeffectsleadtoanincreaseinthenaturalfrequencyofnanobeamsascomparedwiththeclassicalTimoshenkobeammodel.Inaddition,fornanobeamswithlargediameters,thesurfaceeffectsmayincreasethenaturalfrequenciesbyincreasingthethermaleffects.Moreover,withregardtothePasternakelasticfoundation,thenaturalfrequenciesareincreasedslightly.Theresultsofthepresentmodelarecomparedwiththeliterature,showingthatthepresentmodelcancapturecorrectlythesurfaceeffectsinthermalvibrationofnanobeams.

简介：一个纤维节模型基于Timoshenko横梁元素在这研究被建议基于考虑轴的框架元素的非线性的分析，曲折，并且砍变丑。这个模型用砍弯曲被完成相互依赖的明确的表达(SBIF)。元素的形状功能从平衡方程的同类的形式的准确答案被导出因为Timoshenko变丑hypothesis.The建议元素从砍锁是免费的。部分纤维模型与一个多轴的粘性材料模型一起被组成，它被用来模仿每纤维的联合砍轴的非线性的行为。由在纤维之中强加变丑相容性条件，部分、元素的抵抗力量是计算的。因为SBIF形状功能与为节的不同形状的砍修正者因素是交互的，一个反复的过程在建议Timoshenko元素的非线性的州的决心被介绍。另外，建议模型由采用一条corotational坐标转变途径处理几何非线性的问题。为非线性的几何分析的SBIFTimoshenko元素的corotational算法的推导过程被介绍。数字例子证实与一个纤维节模型一起的SBIFTimoshenko元素有象基于灵活性的明确的表达的一样的精确性和坚韧性。最后，SBIFTimoshenko元素被扩大并且demonstratedin一个三维的数字例子。

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