中厚矩形板的振动功率流特性分析  

Vibration power flow analysis of moderately thick rectangular plates

作　　者：薛开[1] 王久法 李秋红[1] 王威远[1] 王平[1] 

机构地区：[1]哈尔滨工程大学机电工程学院,哈尔滨150001

出　　处：《振动与冲击》2013年第21期178-181,共4页Journal of Vibration and Shock

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：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。Considering the effects of shear distortion and rotatory inertia, an improve Fourier series method was employed to analyze power flow of moderately thick rectangular plates with general elastic boundary conditions. The vibration displacements and the cross-sectional rotations of their mid-plane were expressed as the linear combination of a double Fourier cosine series and auxiliary series functions. These supplementary functions were used to solve the discontinuity problems of displacement and rotation partial differentials along edges. So this method was applicable to general elastic boundary conditions. Then, Hamilton＇s principle combined with Mindlin plate theory was adopted to establish a matrix eigenvalue equation equivalent to the governing differential equations of a moderately thick plate. Finally, numerical simulations were performed for the case that a plate was excited with a harmonic point torce, and the spatial distributions of its vibration power flow were obtained.

关 键 词：中厚板 功率流 改进的傅里叶级数 任意弹性边界 HAMILTON原理 

分 类 号：TP533[自动化与计算机技术]