中厚耦合板结构的振动特性分析

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。

Vibration characteristic analysis of moderately thick coupled rectangular plates

Base on Mindlin plate theory, an improve Fourier series method is employed to analyze the vibra-tion of coupled plates with general elastic boundary support and coupled condition. In order to establish gen-eral model, six types of springs are uniformly distributed along coupling edge to simulate the arbitrary cou-pling conditions, and five kinds of springs are uniformly distributed along boundary edge to simulate the ar-bitrary 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 par-tial differentials along the edges. The matrix eigenvalue equation, which is equivalent to governing differ-ential 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 re-sults and the comparisons with both FEA and experiment are presented to validate the correct of the method.