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研究了变厚度圆柱壳自由振动的最大基频设计问题。即在任意轴对称边界条件下,寻求圆柱壳的最优厚度分布使自振基频极大化。利用半解析元方法分析轴对称变厚度圆柱壳的自由振动,将求解自振基频归为求解广义特征值方程,使变厚度圆柱壳的最大基频设计成为极大化最小特征值问题;在此基础上利用适当优化算法求解该优化模型获得变厚度圆柱壳最大基频。典型算例表明了文中方法的有效性和计算程序的快速收敛性。
The maximum fundamental frequency design problem of free vibration of cylindrical shell with variable thickness is studied. That is, under the condition of arbitrary axisymmetric boundary, the optimal thickness distribution of the cylindrical shell is sought to maximize the fundamental frequency of self-vibration. The semi-analytical element method is used to analyze the free vibration of axisymmetric variable thickness cylindrical shell. The fundamental frequency of solution is classified as generalized eigenvalue equation. The maximum fundamental frequency of cylindrical shell with variable thickness is designed to be the minimum and maximum eigenvalue problem. Based on this optimization algorithm, the optimum fundamental frequency of cylinder shell with variable thickness was obtained by using appropriate optimization algorithm. A typical example shows the effectiveness of the proposed method and the fast convergence of the computational program.