耦合板在任意弹性边界条件下的自由振动分析

薛 开;王久法;王威远;李秋红;王 平

振动与冲击 ›› 2013, Vol. 32 ›› Issue (22) : 178-182.

PDF(838 KB)
PDF(838 KB)
振动与冲击 ›› 2013, Vol. 32 ›› Issue (22) : 178-182.
论文

耦合板在任意弹性边界条件下的自由振动分析

  • 薛 开,王久法,王威远,李秋红,王 平
作者信息 +

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

  • XUE Kai,WANG Jiu-fa,WANG Wei-yuanLI Qiu-hong,WANG Ping
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文章历史 +

摘要

采用改进傅立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。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进行比较,验证了本方法的准确性。

Abstract

An improve Fourier series method is employed to analyze the free vibration of coupled plates with general elastic boundary support, in which the vibration displacements is sought as 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. And boundary conditions and coupled conditions are physically realized with the uniform distribution of springs on each boundary edge. Different boundary conditions and coupled conditions can be directly obtained by changing the stiffness of springs. Then Hamilton’s principle can give the matrix eigenvalue equation which is equivalent to governing differential equations of the plate, and all the eigenvalues can be obtained by solving the matrix equation. Finally the numerical results and the comparisons with FEA are presented to validate the correct of the method.




关键词

耦合板 / 自由振动 / 改进的傅立叶级数 / 任意弹性边界 / Hamilton原理

Key words

coupled plates / free vibration / improved Fourier series / general elastic boundary support / Hamilton’s principle

引用本文

导出引用
薛 开;王久法;王威远;李秋红;王 平. 耦合板在任意弹性边界条件下的自由振动分析[J]. 振动与冲击, 2013, 32(22): 178-182
XUE Kai;WANG Jiu-fa;WANG Wei-yuanLI Qiu-hong;WANG Ping. Free vibration analysis of coupled rectangular plates with general elastic boundary support[J]. Journal of Vibration and Shock, 2013, 32(22): 178-182

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