圆形薄板在任意弹性边界条件下的自由振动分析

摘要

采用改进的 Fourier-Bessel 级数方法和 Rayleigh-Ritz 法对任意弹性边界条件下的圆形薄板进行自由振动分析。通过将圆板的位移函数表示为 Fourier-Bessel 级数和辅助级数的组合，有效地解决了位移函数在边界处的不连续性问题。最后，应用 Rayleigh-Ritz 法建立了圆板自由振动的矩阵方程，所有振动参数可以通过求解矩阵方程得到。方程特征值对应着圆板振动的固有频率，特征向量对应着圆板振动的振型模态。通过数值仿真计算结果与文献、有限元结果对比，证明了该方法的正确性。%An improve Fourier-Bessel series method and the Rayleigh-Ritz method are proposed to analyze the free vibration of circular plates with elastically restrained boundary conditions. The vibration displacement is expressed as the superposition of Fourier-Bessel series and auxiliary series functions in the form of the product of polynomial function and cosine series expansion. The use of these supplementary functions is to overcome the discontinuity problems encountered in the displacement partial differentials along the edge. Then the Rayleigh-Ritz method can give the matrix equation of the circular plate,and all the frequency parameters can be easily obtained by solving this matrix equation. The eigenvalues are the nature frequen-cies and the eigenvectors are the modes of the plate. Finally the numerical results and the comparisons with FEA as well as those reported in the literature are presented to validate the correctness of the method.