中厚矩形板的振动功率流特性分析

薛开;王久法;李秋红;王威远;王平

振动与冲击 ›› 2013, Vol. 32 ›› Issue (21) : 178-181.

PDF(1471 KB)
PDF(1471 KB)
振动与冲击 ›› 2013, Vol. 32 ›› Issue (21) : 178-181.
论文

中厚矩形板的振动功率流特性分析

  • 薛开,王久法,李秋红,王威远,王平
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Vibration power flow analysis of moderately thick rectangular plates

  • Xue Kai, Wang Jiufa, Li Qiuhong, Wang Weiyuan,Wang Ping
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摘要

考虑板的横向剪切变形和转动惯量的影响,采用改进Fourier级数的方法对任意弹性边界条件下的中厚矩形板进行振动功率流分析。将板的横向振动位移和转角表示为标准的二维Fourier余弦级数和辅助级数的线性组合。通过辅助级数的引入,解决了位移函数和转角函数的导数在边界不连续的问题,从而使此法适用于任意的弹性边界条件。结合Hamilton原理和Mindlin理论建立求解方程,得到中厚矩形板振动方程的矩阵表达式。最后进行了数值仿真,得到了正弦点力作用下中厚板的功率流场图。

Abstract

Considering the effects of shear distortion and rotator inertia, an improve Fourier series method is employed to analyze power flow of moderately thick rectangular plates with general elastic boundary support. The vibration displacements and the cross-sectional rotations of the mid-plane are 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 and rotations partial differentials along the edges. So this method can be applied to general elastic boundary conditions. Then Hamilton’s principle based on Mindlin plate theory can give the matrix eigenvalue equation which is equivalent to governing differential equations of the plate. Finally numerical analyses are performed for the case where plates are excited by a harmonic point force, and the spatial distributions of vibration power flow are obtained.

关键词

中厚板 / 功率流 / 改进的傅立叶级数 / 任意弹性边界 / Hamilton原理

Key words

moderately thick plates / power flow / improved Fourier series / general elastic boundary support / Hamilton’s principle

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导出引用
薛开;王久法;李秋红;王威远;王平. 中厚矩形板的振动功率流特性分析[J]. 振动与冲击, 2013, 32(21): 178-181
Xue Kai;Wang Jiufa;Li Qiuhong;Wang Weiyuan;Wang Ping. Vibration power flow analysis of moderately thick rectangular plates[J]. Journal of Vibration and Shock, 2013, 32(21): 178-181

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