中厚耦合板结构的振动特性分析  

Vibration characteristic analysis of moderately thick coupled rectangular plates

作　　者：王久法 薛开[2] 李秋红[2] 

机构地区：[1]中国船舶重工集团公司第七一研究所,宜昌443003 [2]哈尔滨工程大学机电工程学院,哈尔滨150001

出　　处：《船舶力学》2016年第5期583-590,共8页Journal of Ship Mechanics

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(HEUCF130701)

摘　　要：基于Mindlin板理论,采用改进傅立叶级数的方法对任意弹性边界条件和耦合条件下的耦合板进行了振动分析。为建立通用的结构模型,在耦合板结构的耦合边上均匀布置六种类型线性约束弹簧模拟耦合条件,在非耦合边上布置五种类型的线性约束弹簧模拟边界条件。耦合板结构的弯曲振动位移函数和面内振动位移函数表示为标准的二维傅立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。利用Hamilton原理建立求解方程,推导出中厚耦合板结构的振动控制方程的矩阵表达式,通过求解矩阵方程可以得到耦合板结构的固有频率和响应。通过数值仿真分析计算,并与有限元结果和实验进行比较,验证了该方法的准确性。Base on Mindlin plate theory, an improve Fourier series method is employed to analyze the vibration of coupled plates with general elastic boundary support and coupled condition. In order to establish general model, six types of springs are uniformly distributed along coupling edge to simulate the arbitrary coupling conditions, and five kinds of springs are uniformly distributed along boundary edge to simulate the arbitrary boundary condition. The vibration displacements of the flexural and in-plane vibration are expressed with the linear combination of a double Fourier cosine series and auxiliary series functions. The use of these supplementary functions is to solve the discontinuity problems which encountered in the displacement partial differentials along the edges. The matrix eigenvalue equation, which is equivalent to governing differential equations of the coupled plate, can be deduced by using Hamilton＇s principle, and the frequencies and response of coupled plates can be obtained by solving the matrix equation. Finally, the numerical results and the comparisons with both FEA and experiment are presented to validate the correct of the method.

关 键 词：耦合板 Mindlin理论 改进的傅立叶级数 任意弹性边界条件 

分 类 号：TP533[自动化与计算机技术]