两端圆板封闭圆柱壳自由振动的半解析解

A semianalytical solution for free vibration of a cylindrical shell with two end plates

文章基于经典弹性板壳理论,通过解析方法导出两端圆板封闭圆柱壳自由振动的求解方程和边界条件。圆柱壳与两端圆板的连接条件由连接处的变形连续性和内力平衡关系得出。应用三角函数和Bessel函数构造该组合壳体的模态振型,对决定任意边界条件圆柱壳模态振型的八次方程的根进行了详细讨论。在MATLAB中编写固有频率的搜索程序,给出了两端圆板封闭圆柱壳自由振动的半解析解。半解析方法得到的固有频率和振型的数值结果与有限元方法计算的结果作了比较,两者几乎完全一致。该半解析方法不存在高频处理难的问题,并且计算速度远远高于有限元方法。

Based on the classical thin plate and shell theory, the basic equations and boundary conditions of a cylindrical shell with two end plates are presented. The conditions of the junction between the cylindrical shell and the two end plates are given by the continuity of deformation and the equilibrium relations near the junction point.The exact and explicit solutions of the mode functions are constructed by using trigonometric and Bessel functions.The roots of an eighthorder algebraic equation which determines the cylindrical shell＇s mode shape with arbitrary boundarys are discussed carefully.A searching algorithm for obtaining natural frequencies is programmed in MATLAB. A semianalytical solution is presented for free vibration of the cylindrical shell with two end plates.The numerical results of natural frequencies and mode shape from semianalytical approach are in agreement well with the results using finite element method. The semianalytical approach greatly reduces the computational time and can handle in highfrequency range as compared to finite element method.