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1、专题论文（SpecialIssues）非线性变速轴向运动黏弹性梁稳态响应王波，陈立群，王洪伟，刘玉敬11,2331.上海大学上海市应用数学和力学研究所，上海2000722.上海大学力学系，上海2004443.宝钢集团苏州冶金机械厂，苏州215151摘要研究了非线性变速轴向运动梁稳态幅频响应。变速轴向运动梁的控制微分方程被建立，黏弹性本构关系引入了物质时间导数，考虑了由均匀轴向运动梁变形的影响而导致梁轴向伸长而引起的附加力，并以轴向张力平均值代替梁上各点的精确值，建立了积分-偏微分非线性轴向运动梁的控制方程。轴向运动梁两端的边界为带有扭转弹簧的套筒铰支的混杂
2、边界条件，同时认为轴向运动速度在平均速度附近做微小简谐脉动。应用渐进摄动法直接求解非线性变速轴向运动梁的控制方程并导出了当扰动速度的频率接近未扰系统任意两个固有频率之和时所发生的组合参数共振的稳态幅频响应方程和振幅方程。数值结果给出了轴向运动梁的黏弹性、扰动振幅、非线性对稳态幅频响应的影响。结果显示，轴向运动梁的材料的黏弹性增大时，零平衡位置的失稳区域会减小；当梁的轴向扰动速度幅值增大时，零平衡位置的失稳区域随之增大；稳定及非稳定的两条非零解曲线的振幅都会因为非线性系数的增大而减小。零解失稳范围则不受非线性项的影响。关键词轴向变速运动梁；黏弹性；渐进法；参
3、数共振；稳态幅频响应中图分类号O32文献标识码A文章编号
1000-7857（2009）02-0025-04axiallymovingbeamswithtime-dependentvelocityisanalyzed.TheAnalysisoftheSteady-StatematerialtimederivativeisusedintheviscoelasticconstitutiveResponseofNonlinearAxiallyrelation.Asymptoticanalysisisproposedtoinvestigatethegovernin
4、gMovingViscoelasticBeamswithequationofanaxiallyacceleratingviscoelasticbeam.Beamsareconstrainedbyelasticjointsatbothendsinalltime.ThesupportingTime-DependentVelocityconditionsmaybeformulatedassimplesupportswithtorsion11,23springs.TheaxialspeedischaracterizedasasimpleharmonicWANGBo
5、,CHENLiqun,WANGHongwei,3variationaboutaconstantmeanspeed.IftheaxialspeedvariationLIUYujingfrequencyapproachesthesumofanytwonaturalfrequencies,thesummationparametricresonancemayoccur.Thestability-state1.ShanghaiInstituteofAppliedMathematicsandMechanics,equationandamplitudeequationa
6、reobtainedforthecombinedShanghaiUniversity,Shanghai200072,Chinaparametricresonanceviatheasymptoticanalysis.Numerical2.DepartmentofMechanics,ShanghaiUniversity,Shanghaiexamplesshowtheeffectsoftheviscoelasticity,theamplitudeof200444,Chinafluctuationandthenonlinearityofthebeamonstabi
7、lity-state3.SuzhouMetallurgicalMachineryPlant,BaosteelGroup,response.Suzhou215151,ChinaKeywordsaxiallyacceleratingbeam;asymptoticanalysis;parametricresonance;viscoelasticity;stability-stateresponseAbstractAxiallyacceleratingbeamscanbeusedtosimulatemanyengineeringdevices.Asaparamet
8、ricvibrationisexcitedbythevariati
