横观各向同性圆柱体自由振动的弹性力学解

本文由横观各向同性的弹性力学方程出发，研究有限长圆柱体的自由振动问题。利用文献「１」的通解，将位移分量和应力分量分别表达成傅里叶－塞尔级数和双曲－贝塞尔级数的形式。通过边界条件和级数的正交关系，得到关于有限长圆柱自由振动频率的特征方程。利用数值方法求解特征根，从而得到圆柱体三维振动的自振频率。

THE ELASTICITY SOLUTION OF THE FREE VIBRATION OF A TRANSVERSELY ISOTROPIC CIRCULAR CYLINDER

In this paper, by the use of the 3D equations of linear elasticity, the free vibration problem of a transversely isotropic finite length circular cylinder is solved. According to the general solution in reference [1], components of the displacements and stresses can be expanded into the Fourier Bessel series and the hyperbolic-Bessel series. Taking advantage of the boundary conditions and the orthogonal relations of the series, the characteristic equation of the natural frequencies of the cylinder is obtained. Solving the characteristic equation numerically, the natural frequencies of the 3D vibration of a finite cylinder circular are thus obtained.