混杂边界条件下轴向变速运动黏弹性梁参数振动的稳定性  

STABILITY ANALYSIS OF PARAMETRIC RESONANCE OF AN AXIALLY ACCELERATING VISCOELASTIC BEAM WITH HYBRID SUPPORTS

作　　者：丁虎[1] 陈立群[1,2] 戈新生[3] 

机构地区：[1]上海应用数学和力学研究所,上海200072 [2]上海大学力学系,上海200444 [3]北京机械工业学院机械工程系,北京100085

出　　处：《振动与冲击》2008年第11期62-63,共2页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(10772092);上海市教育委员会科研项目(07ZZ07);上海市重点学科建设项目(Y0103);上海大学研究生创新基金项目资助(A.16-0101-07-011);北京市自然科学基金项目(1072008)资助项目

摘　　要：研究速度变化的混杂边界条件下轴向运动黏弹性梁参数振动的稳定性。在控制方程的推导中,采用物质导数黏弹性本构关系取代通常采用的只对时间取偏导数的黏弹性本构关系。运用直接多尺度法分析了轴向变速运动混杂边界条件下黏弹性梁的参数振动稳定性,数值结果显示了轴向速度,黏弹性系数以及扭转刚度系数的变化对第一阶亚谐波参数共振失稳区域的影响。Stability of transverse parametric vibration of axially accelerating viscoelastic beam constrained by simple supports with torsion springs was investigated.The governing equation was derived making use of the viscoelastic constitu- tion relation in which,besides the time derivatives,the material derivatives was also taken into account.The method of multiple scales was applied directly to analyze the stability and to determine the instability boundary of parametric reso- nances.Numerical examples show the effects of the constraint stiffness,the mean axial speed,and the viscoelasticity.

关 键 词：轴向运动梁 物质导数 参数共振 稳定性 

分 类 号：O32[理学—一般力学与力学基础]