简介:Inthispaper,afiniteelementmethodisdevelopedtonumericallyevaluatetheshearcoefficientofTimoshenko'sbeamwithmultiplyconneetedcrosssection.Withfocusonanalyzingshearstressesdistributedattheneutralaxisofthebeam,animproveddefinitionoftheshearcoefficientispresented.Basedonthisdefinition,aGalerkin-typefiniteelementformulationisproposedtoanalyzetheshearstressesandsheardeflections.Numericalsolutionsoftheexamplesforsometypicalcross-sectionsarecomparedwiththetheoreticalresults.TheshearcoefficientoftowersectionsoftheTsingMaBridgeiscalculatedbyuseoftheproposedapproach,sothatthefiniteelementmodelingofthebridgecanbedevelopedwiththeaccuratevaluesofthesectionalproperties.
简介:Inthispaper,theboundarystabiligstionoftbeTimoshenkoequationofanononiformbeam,withclarrmpedboundaryconditionatoneendandwitbbendingmomentandshearforcecontrolsattheotherend,isconsidered.Itisprovedthatthesystemisexponentiallystahilizablewhenthebendingmomentandshearforcecontrolsaresimultaneouslyappiied.Thefrequencydomainmethodandthemultipliertechniqueareused.
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: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:ThepresentpaperinvestigatesthedynamicresponseoffiniteTimoshenkobeamsrestingonasixparameterfoundationsubjectedtoamovingload.ItisforthefirsttimethattheGalerkinmethodanditsconvergencearestudiedfortheresponseofaTimoshenkobeamsupportedbyanonlinearfoundation.ThenonlinearPasternakfoundationisassumedtobecubic.Therefore,theefectsofthesheardeformablebeamsandthesheardeformationoffoundationsareconsideredatthesametime.TheGalerkinmethodisutilizedfordiscretizingthenonlinearpartialdifferentialgoverningequationsoftheforcedvibration.ThedynamicresponsesofTimoshenkobeamsaredeterminedviathefourth-orderRunge–Kuttamethod.Moreover,theefectsofdiferenttruncationtermsonthedynamicresponsesofaTimoshenkobeamrestingonacomplexfoundationarediscussed.ThenumericalinvestigationsshowsthatthedynamicresponseofTimoshenkobeamssupportedbyelasticfoundationsneedssuperhigh-ordermodes.Furthermore,thesystemparametersarecomparedtodeterminethedependenceoftheconvergencesoftheGalerkinmethod.
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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。
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.
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