变厚度圆柱壳的最大基频设计

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.

Maximizing Fundamental Frequency of a Thin Cylindrical Shell with Various Thickness

The optimization of cylindrical shells on fundamental frequency is investigated in this paper. Maximizing fundamental frequency of a thin cylindrical shell on free vibration is considered with arbitrary axisymmetric boundary conditions and the constant volume.The objective function of the model is to maximize the fundamental frequency of the cylindrical shell.Fundamental frequency of cylindrical shell is obtained by the finite element method.The optimal designs are reduced to nonlinear programming problems with an equality constraint. In maximizing the fundamental frequency, the position of the fundamental frequency from a previous iteration is used as the next initial value. The complex search (Box algorithm) is employed to solve the optimization problem. This procedure converges quickly and numerical results show the effectiveness of the method. Several examples are provided to illustrate the method.