变厚度薄板在任意弹性边界条件下的自由振动分析  

Free vibration analysis of tapered plates with arbitrary elastic boundary condition

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21期131-135,共5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单向变厚度薄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,改进后的位移函数能够同时满足位移边界条件和力的边界条件。边界条件通过均匀布置的线性位移弹簧和旋转弹簧来模拟,改变弹簧刚度值可以实现不同边界条件的模拟。利用Hamilton原理和Rayleigh-Ritz法建立求解方程,得到变厚度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和振型。通过数值仿真分析计算并与有限元及文献的结果进行比较,验证了本方法的准确性。An improve Fourier series method was employed to analyze the free vibration of tapered plates with arbitrary elastic boundary condition. With this method, 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, the improved displacement functions satisfied both displacement and force boundary conditions. Boundary conditions were physically realized with the uniform distributions of transverse displacement and rotational springs along each boundary edge. Different boundary conditions were directly obtained by changing the stiffnesses of springs. Then, Rayleigh-Ritz method based on Hamilton＇s principle was used to build a matrix equation equivalent to the governing differential equations of a tapered plate, and the eigenvalues and eigenvectors were obtained by solving the matrix equation. Finally, the comparisons among numerical simulation results, those obtained with FEM and those reported in literatures were presented to validate the correctness of the proposed method.

关 键 词：变厚度薄板 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]