轴向运动功能梯度粘弹性梁横向振动的稳定性分析  

STABILITY ANALYSIS ON TRANSVERSE VIBRATION OF AXIALLY MOVING FUNCTIONALLY GRADED VISCOELASTIC BEAMS

作　　者：刘金建[1] 蔡改改[1] 谢锋[1] 黄伟国[1] 李成[1] 

机构地区：[1]苏州大学城市轨道交通学院,苏州215131

出　　处：《动力学与控制学报》2016年第6期533-541,共9页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(51405320;51405321);江苏省自然科学基金(BK20140339;BK20130303);江苏省高校自然科学研究面上项目(14KJB460023);苏州市科技计划项目(SYG201537)~~

摘　　要：基于Euler梁理论研究了轴向运动功能梯度粘弹性梁横向振动的稳定性问题.基于问题的数学模型和控制方程,利用微分求积法求得了轴向匀速运动功能梯度粘弹性梁亚临界区域内横向振动的复频率,分析其随着轴向运动速度、材料梯度指数等参数的变化情况,探讨上述参数对超临界区域失稳形式的影响.然后应用多尺度法结合边界条件分析了轴向速度带有周期扰动成分的变速运动功能梯度粘弹性梁的失稳问题,重点讨论了当速度扰动频率为固有频率二倍或者为两固有频率之和/差时所发生的次谐波共振及组合共振所导致的失稳.数值算例表明,随着梯度指数的增大,匀速运动功能梯度粘弹性梁的临界发散速度、耦合速度以及变速运动功能梯度粘弹性梁的稳定区域减小,且粘弹性系数的影响逐渐变弱,同等条件下,轴向运动功能梯度粘弹性固支梁比简支梁更为稳定.The stability of the transverse vibration of an axially moving functionally graded viscoelastic beam （FGVB） is studied based on the Euler beam theory. The complex frequencies of FGVB are firstly investigated by the differential quadrature method, where the main parameters such as axial speed and gradient index are considered. The effects of the axial speed and gradient index on the vibration characteristics and instable forms in super critical region are also examined. Subsequently, the instability behaviors of FGVB with periodic perturbational velocity are addressed using the method of multiple scales and specific boundary conditions. The discussion is then mainly focused on the instable regions caused by summation resonance and sub harmonic resonance, respectively, where the resonance occurs when the harmonic frequency approaches the sum or difference of any two mode natural frequencies. It is shown that the critical divergence and flutter velocities of the uniformly moving beam, as well as the stability regions of non uniformly moving beam decrease with the increase of gradient index, and the viscoelastic effect becomes weaker with increasing gradient index. Moreover, the stability regions of axially moving FGVB for fully clamped boundary condition are larger than those for the simply supported case.

关 键 词：轴向运动 功能梯度粘弹性梁 稳定性 次谐波共振 组合共振 

分 类 号：O327[理学—一般力学与力学基础]