旋转粘弹性夹层梁非线性自由振动特性研究  

VIBRATION ANALYSIS OF ROTATING VISCOELASTIC SANDWICH BEAM

作　　者：蒋宝坤[1] 李映辉[1] 李亮[1] 

机构地区：[1]西南交通大学力学与工程学院,成都610031

出　　处：《动力学与控制学报》2013年第3期241-245,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11072204);中央高校基本科研业务费专题项目(SWJTU11ZT15)~~

摘　　要：对旋转粘弹性夹层梁的非线性自由振动特性进行了分析.基于Kelvin-Voigt粘弹性本构关系和大挠度理论,建立了旋转粘弹性夹层梁的非线性自由振动方程,并使用Galerkin法将偏微分形式振动方程化为常微分振动方程.采用多重尺度法对非线性常微分振动方程进行求解,通过小参数同次幂系数相等获得微分方程组,并通过求解方程组及消除久期项来获得旋转粘弹性夹层梁非线性自由振动的一次近似解.用数值方法讨论了粘弹性夹层厚度、转速和轮毂半径对梁固有频率的影响.结果表明:固有频率随转速增大而增大,随夹层厚度增大而减小,随轮毂半径的增大而增大.The nonlinear free vibration analysis of rotating viscoelastic sandwich beam is presented in this article. The control equation of the rotating viscoelastic sandwich beam was established based on Kelvin-Voigt constitutive equation and large deflection theory. Partial differential equation of vibration was transformed into an ordinary differ- ential one using Galerkin method. The ordinary differential equation of nonlinear vibration was solved by multiple scale method. Systems of equations were obtained by comparing coefficient of power of the micro parameter. First ap- proximate solution of the nonlinear free vibration of rotating viscoelastic sandwich beam could be acquired by solving the systems of equations as well as eliminating the secular terms. Numerical simulation was used to discuss the effect of thickness of the sandwich layer, variation of rotating velocity and radius of the hub on nature frequency. The results indicated that natural frequency of the rotating viscoelastic sandwich beam increased with the increase of rotating velocity and radius of the hub while decreased with the increase of thickness of the sandwich layer.

关 键 词：旋转粘弹性夹层梁 Kelvin—Voigt 非线性振动 多重尺度法 近似解 固有频率 

分 类 号：O322[理学—一般力学与力学基础]