简介：Afinitedifferencemethodispresentedtosimulatetransversevibrationsofanaxiallymovingstring.Bydiscretizingthegoverningequationandtheequationofstress-strainrelationatdifferentfrictionalknots,twolinearsparsefinitedifferenceequationsystemsareobtained.Thetwoexplicitdifferenceschemescanbecalculatedalternatively,whichmakethecomputationmuchmoreefficient.Thenumericalmethodmakesthenonlinearmodeleasiertodealwithandoftruncationerrors,O(Δt~2+Δx~2).Italsoshowsquitegoodstabilityforsmallinitialvalues.Numericalexamplesarepresentedtodemonstratetheefficiencyandthestabilityofthealgorithm,anddynamicanalysisofaviscoelasticstringisgivenbyusingthenumericalresults.

简介：为有一个横向的裂缝的一条半长带的飞机橡皮问题被调查。起始的问题被一个不可分的转变方法的使用与一个概括计划归结为一个一个维的连续问题。一个维的问题首先作为一个向量边界问题被提出，然后归结为三个单个不可分的方程(SIE)的一个系统。系统被一个直角的多项式方法和一个特殊概括方法的使用解决。这个工作的贡献是核的考虑在解决系统的固定奇特。相对半长带的裂缝长度和它的地点侧面的方面被调查简化问题陈述。这简化把起始的问题归结为二SIE的一个系统。

简介：Theprincipleand1:3internalresonanceofarectangularthinplateinatransversemagneticfieldisinvestigated.Basedonthemagneto-elasticvibrationequationandelectromagneticforceexpressionsofthethinplates,thenonlinearmagneto-elasticvibrationdifferentialequationsofrectangularplatesunderexternalexcitationinatransversemagneticfieldarederived.Forarectangularplatewithonesidefixedandthreeothersidessimplysupported,thetwo-degree-offreedomnonlinearDuffingvibrationdifferen-tialequationsareproposedbythemethodofGalerkin.Themethodofmultiplescalesisadoptedtosolvethemodelequationsandobtainfourfirst-orderordinarydifferentialequationsgoverningmodulationoftheamplitudesandphaseanglesinvolvedviathefirst-orderorthesecond-orderprimary-internalreso-nances.Withanumericalexample,theamplitudefrequencyresponsecurves,timehistoryresponses,phaseportraitsandPoincaremapsofthefirsttwoordervibrationmodesviaprinciple-internalresonancearerespectivelycaptured.Andtheeffectsofexternalexcitationamplitudes,magneticfieldintensitiesandthicknessesonthevibrationofsystemarediscussed.Theresultsshowthattheresponseisdominatedbythelowmodewhenprinciple-internalresonanceoccurs.Theinternalresonanceprovidesamechanismfortransferringenergyfromahighmodetoalowmode.

简介：Ritzmethodisaneffectivewaywidelyusedtoanalyzethetransversebendingofthinrectangularplates.Itsaccuracydependscompletelyonthebasisfunctionsselected.Thispaperselectsthesuperpositionofsineserieswithpolynomialsasthebasisfunctionsofthinrectangularplates.Thecalculatingformulaearenotonlysimpleandeasilyprogrammed,butalsohavehighaccuracy.Finally,twonumericalresultsaregivenandcomparedwiththoseobtainedbytheclassicalmethod.

简介：Basedonthevariationandharmonicequationsandbytakingthemaximumamplitudeoftheshellcenterastheperturbationparameter,nonlinearvibrationofthinshallowconicshellsundercombinedactionofperipheralmomentandtransverseloadswassolved.Thelinearnaturalfrequencycanbegotbythefirst-orderapproximationandthemoreaccuratenonlinearfrequencyisgotbythesecond-orderapproximationundertheactionofstaticloads.Meanwhilethethird-orderapproximateanalyticexpressionisgivenfordescribingthenonlinearrelationbetweennaturefrequencyandperipheralmoment,transverseloads,amplitude,baseangleunderthesmalldeformation.Withinsomerange,thecomplexandregularityofthenonlinearrelationcanbedirectlyobservedfromthenumericresults.

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