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。最后进行数值计算并与现有的文献结果进行比较,验证了该方法的快速收敛性和计算精确性。
An improved Fourier series method was proposed to develop the transverse vibration model of orthotropic rectangular plates and derive the matrix equation which is equivalent to governing differential equations. An analytical solution for vibration of plates with general elastic boundary conditions was provided. The vibration displacement was solved as the linear combination of a double Fourier cosine series and an auxiliary series. The use of these supplementary series is to solve the discontinuity problem encountered in the partial differentials of displacement function along the edges.The vibration mode characteristics were obtained by solving the eigen values of the matrix. Several numerical examples were given and the comparison of the results with those of the available literature validates the convergence and correctness of the method.
出处
《振动与冲击》
EI
CSCD
北大核心
2015年第24期123-127,143,共6页
Journal of Vibration and Shock
