齐次边界条件下圆柱壳的自由振动研究

摘要

The study of circular cylindrical shells under arbitrary boundary conditions is provided,based on Fliigge thin shell theory.The frequency can be obtained from motion control equations and boundary condition equations.An exact displacement expression is used for analysis.The sweep frequency skill is utilized for finding the roots of corresponding equation which derived from those two characteristic equations.The zeros of this equation are the frequencies of shells depending on specific boundaries in both ends.The dispersions plots of shells are studied together with boundary conditions.From the analysis,the frequency-wave points are located on the purely imaginary part of dispersion plot for arbitrary boundary conditions.The main procedure of wave propagation approach is also discussed for vibrations of shells.The total frequency domain could be divided into 3 parts,which corresponding to 3 vibration types of shells.Numerical examples are provided in this paper for demonstration of present analysis procedure.%基于Flügge弹性薄壳理论研究圆柱壳在齐次边界条件下的自由振动问题.圆柱壳的自振频率通过位移控制方程和边界条件控制方程联立求解获得.引入一般形式的位移函数之后,位移控制方程能够得到关于频率和波数的频散图,联合边界条件后转化为8阶矩阵行列式的零点求解.讨论自振频率点在频散曲线中的位置,给出纯虚数曲线分支的含义.还讨论精确解和常用梁方法的联系,研究振型在3个频率区域变化的情况.