耦合板在任意弹性边界条件下的自由振动分析  

Free vibration analysis of coupled rectangular plates with general elastic boundary conditions

作　　者：薛开[1] 王久法 王威远[1] 李秋红[1] 王平[1] 

机构地区：[1]哈尔滨工程大学机电工程学院,哈尔滨150001

出　　处：《振动与冲击》2013年第22期178-182,188,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(51105087);中央高校基本科研业务费专项资金资助(HEUCF110701)

摘　　要：采用改进傅里叶级数的方法对任意弹性边界条件下的耦合板进行自由振动分析,将板的振动位移函数表示为标准的二维傅里叶余弦级数和辅助级数的线性组合。通过辅助级数的引入,解决了位移导数在边界不连续的问题。边界条件和耦合条件通过均匀布置的线性位移弹簧和旋转弹簧来模拟,通过改变弹簧刚度值可以实现任意边界条件和耦合条件的模拟。利用Hamilton原理建立求解方程,建立一个线性方程组,最终得到耦合板的控制方程的矩阵表达式,通过特征值分解可以求得固有频率。通过数值仿真分析计算并与有限元结果比较,验证该方法的准确性。An improve Fourier series method was employed to analyze the free vibration of coupled plates with general elastic boundary conditions. Their vibration displacements were expressed as the linear combination of a double Fourier cosine series and auxiliary series functions. These supplementary functions were used to solve the discontinuity problems of displacement partial differentials along edges. Boundary conditions and coupled conditions were physically realized with the uniform distributions of springs along each boundary edge. Different boundary conditions and coupled conditions were directly obtained by changing the stiffnesses of springs. Then, Hamilton＇s principle was used to build a matrix eigenvalue equation equivalent to the governing differential equations of a coupled plate, and all the eigenvalues were obtained by solving the matrix equation. Finally, the comparison between the numerical results and those obtained with FEM was presented to validate the correctness of the proposed method.

关 键 词：耦合板 自由振动 改进的傅里叶级数 任意弹性边界 HAMILTON原理 

分 类 号：TP533[自动化与计算机技术]