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.
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简介:在这份报纸,我们在场解决合并接触线状况的一个阶段地模型的一个有效精力马厩计划。而不是通常使用的Cahn-Hilliard类型阶段方程,我们与与Navier边界状况结合了不可压缩的海军司烧方程的静态的接触线边界条件收养Allen-Cahn类型阶段地模特儿。设计方法被用来处理海军司烧方程,辅助功能为非凸的Ginzburg四轮马车体积潜力被介绍。我们证明计划是线性的,decoupled和精力马厩。而且,我们证明那个充分分离的计划也是精力稳定。一个有效有限元素空间discretization方法被实现验证建议计划的精确性和效率。数字结果证明建议计划很有效、精确。