正交各向异性矩形薄板振动的一种半解析方法

使用半解析的多项康氏法分析对边简支、对边固定和对边固定-简支的正交各向异性矩形薄板振动问题。选择多个梁特征函数作为试函数,精确满足对边所有边界条件。通过Gakerkin积分将偏微分振动方程转化为常微分方程组并整理为状态方程形式。强迫满足另一对边的边界条件,获得频率方程,确定固有频率。文献结果比较不仅证实了该方法的有效性,而且揭示通过该方法获得的对边简支板的解是精确解。最后,研究了不同长宽比下试函数项数对无量纲固有频率的影响。

One Computational Method of the Eigenvalues of the Horizontal Vibration Problem of Beam

This paper considers one computational method of the eigenvalues approximate value of the horizontal vibration problem of beam. The proof of our main result is based on the variational formula. First of all, Cauchy inequality is used to obtain a basic inequality. Secondly, the functions of basis are made by Galerkin method, and the error estimates of eignevalues are obtained by Cauchy inequality. At last, the computational method of the approximate value of the eigenvalues turns out immediately, and acc...