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该文阐述了将动力刚度法应用于中厚圆柱壳的自由振动分析。从考虑横向剪切变形和转动惯量的中厚壳理论出发,将圆柱壳的振动分解为一系列确定环向波数下的一维振动问题。用常微分方程求解器COLSYS求解该一维问题的动力刚度,通过Wittrick-Williams算法及导护型牛顿法求得该环向波数下结构的频率和振型。由于求解动力刚度时使用COLSYS对控制方程进行了精确求解,所以该文方法是精确方法。数值算例验证了中厚圆柱壳壳段固端频率计数J0计算方法的可靠性。综合表明:应用动力刚度法对中厚圆柱壳自由振动进行分析是可靠、精确的。
This paper describes the application of dynamic stiffness method to free vibration analysis of medium-thick cylindrical shells. Based on the medium-thick shell theory, which considers transverse shear deformation and moment of inertia, the vibration of the cylindrical shell is decomposed into a series of one-dimensional vibration problems that determine the circumferential wavenumber. Using the ordinary differential equation solver COLSYS to solve the dynamic stiffness of the one-dimensional problem, the frequency and mode shapes of the structure under the circumferential wavenumber are obtained by the Wittrick-Williams algorithm and the guided-guard Newton method. Since the governing equations are solved accurately using COLSYS in solving dynamic stiffness, this method is an accurate method. The numerical example verifies the reliability of the method for calculating the frequency J0 of the solid end of a thick cylindrical shell. The results show that it is reliable and accurate to use the method of dynamic stiffness to analyze the free vibration of the medium-thick cylindrical shell.