密封容器组合壳自由振动的精确解

给出了一类密封容器组合壳自由振动问题的精确解，基于Love经典薄壳理论，导出了具有任意经线形状的旋转壳体在轴对称振动时的基本方程，组合壳结构中球壳与柱壳的连接条件是通过连接处的变形连续性和内力平衡关系得出的。问题的数学模型被归结为常微分方程组在球壳和 壳两个区间上的特征值问题。振动模态函数是由Legendre和三角函数构造出来，并且得到了精确的频率方程。所有的计算都是在Maple程序下运行的，无论是精确的符号运算还是具有所需有效数学精度的数值计算，都表明该文所编译的Maple程序是简单而有效的。固有频率的数值结果同文献中有限元法和其它数值方法的结果作了比较。作为一个标准，该文给出的精确解对于检验各种近似方法的精密度是有价值的。

-Hermetic Capsule

An exact analytical solution was presented for free vibration of composite shell structure_hermetic capsule. The basic equations on axisymmetric vibration were based on the Love classical thin shell theory and derived for shells of revolution with arbitrary meridian shape. The conditions of the junction between the spherical and the cylindrical shell segments are given by the continuity of deformation and the equilibrium relations near the junction point. The mathematical model of problem is reduced to as an eigenvalue problem for a system of ordinary differential equations in two separate domains corresponding to the spherical and the cylindrical shell segments. By using Legendre and trigonometric functions, exact and explicitly analytical solutions of the mode functions were constructed and the exact frequency equation were obtained. The implementation of Maple programme indicates that all calculations are simple and efficient in both the exact symbolic calculation and the numerical results of natural frequencies compare with the results using finite element methods and other numerical methdos. As a benchmark, the exactly analytical solutions presented in this paper is valuable to examine the accuracy of various approximate methods.