黏弹性轴向运动梁非线性受迫振动稳态幅频响应  

Steady-state Response of Non-linear Forced Vibration of Axially Moving Viscoelastic Beams

作　　者：丁虎[1] 陈立群[1,2] 戈新生[3] 

机构地区：[1]上海市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：《力学季刊》2008年第3期502-505,共4页Chinese Quarterly of Mechanics

基　　金：国家杰出青年科学基金(10725209);国家自然科学基金(10772092);上海市教育委员会科研项目(07ZZ07);上海市重点学科建设点项目(Y0103);上海大学研究生创新基金(A.16-0101-07-011);北京市自然科学基金(1072008)

摘　　要：本文研究了黏弹性轴向运动梁横向受迫振动稳态幅频响应问题。在控制方程的推导中,对黏弹性本构关系采用物质导数。把多尺度法直接应用于梁横向振动的非线性控制方程,利用可解性条件消除长期项,得到系统稳态的幅频响应曲线。运用Lyapunov一次近似理论分析幅频响应曲线的稳定性。通过算例研究了黏性系数,外部激励幅值以及非线性项系数对稳态幅频响应曲线及其稳定性的影响。运用数值方法对两端固定边界下黏弹性轴向运动梁的控制方程直接数值解,分析梁横向非线性振动的稳态幅频响应,通过数值算例验证直接多尺度法的结论。Forced vibration was investigated for axially moving viscoelastic beams. The governing equation was derived from the viscoelastic constitution relation by using material derivative. The method of multiple scales was applied to the mathematical model to calculate the steady state response. The equation of response curves was derived from the solvability condition of eliminating secular terms. The stability of steady state responses was analyzed by use of Lyapunov linearized stability theory. The finite difference schemes were developed to solve the equation of axially moving viscoelastic beams with fixed supports for steadystate response. Numerical examples are presented to highlight the effects of non - linear coefficient, the excitation amplitude, and viscosity coefficient.

关 键 词：轴向运动梁 黏弹性 物质导数 受迫振动 有限差分法 

分 类 号：O32[理学—一般力学与力学基础]