求解直边简支环扇板振动特性的积分方程方法

将傅里叶－贝塞尔级数引入积分方程方法，推导出一种研究沿直边简支环扇形板结构振动特性的简捷，高效的积分方程方法，根据积分方程和傅里叶一贝塞尔级数理论，首先采用由第一、二类贝塞尔函数组成的完备正交函数系构造直边简支环扇板的格林函数，然后由叠加原理将环扇形板的自由振动问题转化为积分方程特征值问题；进而将积分方程形式的特征值问题转化为无穷阶正定对称矩阵的标准特征值问题，计算结果表明，该方法不仅运算简捷，精度高，适用性强，而且为分析更为复杂的环扇板的振动问题提供可靠的基础。

INTEGRAL EQUATION METHOD FOR VIBRATION CHARACTARISTICS OF ANNULAR SECTORIAL PLATES WITH SIMPLY- SUPPORTED RADIAL EDGES

A both brief and effective integral equation method is given by combining the approach of integral equations and the Fourier series method in structure mechanics. Basing on the theory of integral equation and Fourier-Bessel function,a type of complete systems of orthogonal functions, which is consisted of Bessel functions of the first and the second kinds, is introduced into the construction of Green's function of annular sector plate with simply-supported radial edges. Then the eigenvalue problem of free vibration of annular sector plates is transformed into the eigenvalue problem of integral equation by using superposition theorem. And then the eigenvalue problem of integral equation is transformed into the standard eigenvalue problem of a positive definite matrix with infinite order. The results obtained not only reveal its briefness, high precision, and its extensiveness but also provide a reliable premise for the vibration analysis of more complex annular sector plates.