正交各向异性矩形板的自由振动特性分析

曾军才1,王久法1,姚望2,于涛2

振动与冲击 ›› 2015, Vol. 34 ›› Issue (24) : 123-127.

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (24) : 123-127.
论文

正交各向异性矩形板的自由振动特性分析

  • 曾军才1,王久法1,姚望2,于涛2
作者信息 +

Free vibration characteristic analysis of orthotropic rectangular plates

  • Zeng Juncai1, Wang Jiufa1, Yao Wang2, Yu Tao2
Author information +
文章历史 +

摘要

采用改进Fourier级数方法,建立了正交各向异性矩形薄板的弯曲振动模型,推导出与振动控制方程等价的矩阵方程,得到控制方程在任意边界条件下的解析解。弯曲振动的位移函数表示为标准的二维Fourier余弦级数和辅助Fourier级数之和,通过辅助级数的引入,解决了振动位移函数的偏导数在各边界处潜在不连续的问题。矩形板的振动模态信息能够通过求解一个标准的矩阵特征值而得到。最后进行了数值计算并与现有的文献结果进行比较,验证了本方法的快速收敛性和计算精确性。

Abstract

Improved Fourier series method is proposed to develop the transverse vibration model of orthotropic rectangular plates and derive the matrix equation which is equivalent to governing differential equations, the analytical solution for vibration of plate with general elastic boundary condition is obtained. The vibration displacement is sought as the linear combination of a double Fourier cosine series and auxiliary series functions. The use of these supplementary series is to solve the discontinuity problems which encountered in the displacement partial differentials along the edges. The vibration mode characteristics can be obtained by solving the matrix equation. Finally several numerical examples are given and the comparisons with available literature to validate the convergence and correct of the method.

关键词

正交各向异性板 / 改进Fourier级数 / 任意弹性边界条件 / 解析解

Key words

orthotropic plates / improved Fourier series / general elastic boundary support / analytic solution

引用本文

导出引用
曾军才1,王久法1,姚望2,于涛2. 正交各向异性矩形板的自由振动特性分析[J]. 振动与冲击, 2015, 34(24): 123-127
Zeng Juncai1, Wang Jiufa1, Yao Wang2, Yu Tao2. Free vibration characteristic analysis of orthotropic rectangular plates[J]. Journal of Vibration and Shock, 2015, 34(24): 123-127

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