简介：ApplyingLagrange–Germain'stheoryofelasticthinplatesandHamiltonianformulation,thedynamicsofcantileverplatesandtheproblemofitsvibrationcontrolarestudied,andageneralsolutionisfinallygiven.BasedonHamiltonianandLagrangiandensityfunction,wecanobtaintheflexuralwaveequationoftheplateandtherelationshipbetweenthetransverseandthelongitudinaleigenvalues.Basedoneigenfunctionexpansion,dispersionequationsofpropagationmodeofcantileverplatesarededuced.Bysatisfyingtheboundaryconditionsofcantileverplates,thenaturalfrequenciesofthecantileverplatestructurecanbegiven.Then,analyticsolutionoftheprobleminplatestructureisobtained.Anhybridwave/modecontrolapproach,whichisbasedonbothindependentmodalspacecontrolandwavecontrolmethods,isdescribedandadoptedtoanalyzetheactivevibrationcontrolofcantileverplates.Thelow-order(controlledbymodalcontrol)andthehigh-order(controlledbywavecontrol)frequencyresponseofplatesarebothimproved.Thecontrolspilloverisavoidedandtherobustnessofthesystemisalsoimproved.Finally,simulationresultsareanalyzedanddiscussed.

简介：有多重时间延期的一个灵活伸臂盘子的活跃控制用分离最佳的控制方法被调查。有多重时间延期的一个控制器被介绍。在这个控制器，时间延期效果在整个控制设计和没有近似在动态系统的数学模型被合并，假设在控制器推导被做，因此系统稳定性容易被保证。而且，这个控制器为两小时间延期和大时间延期是可得到的。建议控制器的可行性和效率这份报纸最后通过数字模拟被验证。

简介：Theseriescomposedbybeammodefunctionisusedtoapproximatethedisplacementfunctionofconstraineddampingoflaminatedcantileverplates,andthetransversedeformationoftheplateonwhichaconcentratedforceisactediscalculatedusingtheprincipleofvirtualwork.BysolvingLagrange'sequation,thefrequenciesandmodellossfactorsoffreevibrationoftheplateareobtained,thenthetransientresponseofconstraineddampingoflaminatedcantileverplateisobtained,whentheconcentratedforceiswithdrawnsuddenly.Thetheoreticalcalculationsarecomparedwiththeexperimentaldata,theresultsshow:boththefrequenciesandtheresponsetimeoftheoreticalcalculationanditsvariationallawwiththeparametersofthedampinglayerareidenticalwithexperimentalresults.Also,theresponsetimeofsteelcantileverplate,unconstraineddampingcantileverplateandconstraineddampingcantileverplatearebroughtintocomparison,whichshowsthattheconstraineddampingstructurecaneffectivelysuppressthevibration.

简介：扣环/脆裂声并且弯曲并且为伸臂联合矩形的软铁磁性的盘子magneto-elastic-plastic相互作用的行为的分析被介绍。为塑料从铁磁性的盘子，薄盘子的弄弯并且弯曲的理论，协定收益标准和增长理论的变化原则基于磁性的力量的表示变丑，我们建立数字代码到份量上模仿行为非线性地由有限元素方法的多地联合问题。与扣环/脆裂声并且弯曲的现象一起，或偏转的典型曲线对应用磁场的大小数字地正在被显示，批评大量扣环/脆裂声，并且塑料变丑的影响和这些批评负担上的板的宽度，与应用磁场的大小膨胀的塑料区域，以及板的偏转配置的发展数字地在案例研究被获得。

简介：Bygivingupanyassumptionsaboutdisplacementmodelsandstressdistribution,themixedstateHamiltonequationfortheaxisymmetricproblemofthethicklaminatedclosedcantilevercylindricalshellsisestablished.Anidenticalanalyticalsolutionisobtainedforthethin,moderatelythickandthicklaminatedclosedcantilevercylindricalshells.Allequationsofelasticitycanbesatis-fied,andallelasticconstantscanbetakenintoaccount.

简介：Vibrationmodeoftheconstraineddampingcantileverisbuiltupaccordingtothemodesuperpositionoftheelasticcantileverbeam.ThecontrolequationoftheconstraineddampingcantileverbeamisthenderivedusingLagrange'sequation.Dynamicresponseoftheconstraineddampingcantileverbeamisobtainedaccordingtotheprincipleofvirtualwork,whentheconcentratedforceissuddenlyunloaded.Frequenciesandtransientresponseofaseriesofconstraineddampingcantileverbeamsarecalculatedandtested.Influenceofparametersofthedampinglayerontheresponsetimeisanalyzed.Analyitcalandexperimentalapproachesareusedforverification.Theresultsshowthatthemethodisreliable.

简介：Dynamicmodelingofacantileverbeamunderanaxialmovementofitsbasementispresent-ed.ThedynamicequationofmotionforthecantileverbeamisestablishedbyusingKane’sequationfirstandthensimplifiedthroughtheRayleigh-Ritzmethod.Comparedwiththeoldermodelingmethod,whichlineari-zesthegeneralizedinertiaforcesandthegeneralizedactiveforces,thepresentmodehngtakesthecoupledcubicnonlinearitiesofgeometricalandinertialtypesintoconsideration.Themethodofmultiplescalesisusedtodirectlysolvethenonlineardifferentialequationsandtoderivethenonlinearmodulationequationfortheprincipalparametricresonance.Theresultsshowthatthenonlinearinertiatermsproduceasofteningeffectandplayasignificantroleintheplanarresponseofthesecondmodeandthehigherones.Ontheotherhand,thenonlineargeometrictermsproduceahardeningeffectanddominatetheplanarresponseofthefirstmode.Thevalidityofthepresentmodelingisclarifiedthroughthecomparisonsofitscoefficientswiththoseexperimentallyverifiedinpreviousstudies.

简介：Owingtotheabsenceofproperanalyticalsolutionofcantileverbeamsforcouplestress/straingradientelas-to-plastictheory,experimentalstudiesofthecantileverbeaminthemicro-scalearenotsuitableforthedeterminationofmateriallength-scale.Basedonthecouplestresselasto-plas-ticity,ananalyticalsolutionofthincantileverbeamsisfirstlypresented,andthesolutioncanberegardedasanextensionoftheelasticandrigid-plasticsolutionsofpurebendingbeam.Acomparisonwithnumericalresultsshowsthatthecurrentanalyticalsolutionisreliableforthecaseofσ0(?)H(?)E,whereσ0istheinitialyieldstrength,HisthehardeningmodulusandEistheelasticmodulus.Fortunately,theabovementionedconditioncanbesatisfiedformanymetalmaterials,andthusthesolutioncanbeusedtodeterminethemateriallength-scaleofmicro-structuresinconjunctionwiththeexperimentofcantileverbeamsinthemicro-scale.

简介：StraightandBentnano-cantileverspecimensarerespectivelyproposedtoinvestigatethesingle-modeandmixed-modecrackinitiationattheCu/Siinterfaceedgeinnanoscalecomponents.Withaminuteloadingapparatus,allnanoscalesamplesareinsituloadedandobserved.Numericalanalysisisemployedtoacquirethecriticalinterfacialstressdistributionsduringcrackinitiation.ThestressconcentrationregionsneartheedgeofCu/Siinterfaceinallspecimensarewithinthescaleof100nm,andthecriticalnormalandshearstresseshaveacircularrelationinnanoscalecomponents,whichrepresentsthefracturecriterionoftheinterfaceinnanoscalecomponents.

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简介：Thispaperdealswithfinitedeformationproblemsofcantileverbeamwithvariablesec-tionundertheactionofarbitrarytransverseloads.Bytheuseofamethodofvariablereplacement,thenonlineardifferentialequationwithvariedcoefficientfortheproblemcanbetransformedintoanequationwithvariableseparable.Theexactsolutioncanbeobtainedbytheintegrationmethod.Someexamplesaregiveninthepaper,andtheresultsoftheseexamplesshowthatthisexactsolutionincludestheexistingsolutionsinreferencesasspecialcases.

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简介：这个工作学习在横梁的免费结束由非一致地分布式的连续负担和集中的负担组成的受到联合装载的苗条、非棱柱的伸臂横梁的大偏转。伸臂的材料被假定非线性地有弹性。在在张力、压缩的领域的应力和紧张之间的不同非线性的关系被考虑。数字答案的精确性被从以前的研究并且与一个实验室实验把他们与结果作比较评估。