机械动力优化设计的摄动逆求法及其应用

本文利用广义特征值的摄动（扰动）特性和逆求的思想提出一个机械动力（态） 优化设计方法，用以求解带频率禁区（含特征方程隐式性能约束）的动力优化设计问 题．给出了本方法可行性的论证。文后举了一个２５维设计变量的飞机发动机转子系 统动力优化设计实例。用数学规划和本文摄动逆求相结合方法求解，重分析５－６次即可。方法直观，程序简单．木方法亦可能推广应用于工程结构优化设计。

The Method of Perturbation Converse Solution for Optimal Dynamic Design and Its Application

In this paper, an optimal dynamic design method, based on the idea o perturbation characteristic of generalized eigenvalues and converse solution, is presented, With it, the problems of optimal dynamic design with unacceptable frequency band (involving eigenvalue equation with implicit behaviour constra-ints) can be solved, The idea of this method is that, as soon as the behaviour constraints of unacceptable frequency band are violated, an unacceptable band of the evading variable is set, By means of the perturbation characteristic of generalized eigen- values and the known frequeucy increment that can avoid the unacceptable frequency band, the changes of the elements of stiffness matrix and mass matrix in eigenvalue equation can conversely be calculated. Then the changes of the design variables can be determined, hence the aim of avoiding unacceptable frequency band can be achieved, So the solution of eigenvalue equation with implicit behaviour constraints can be avoided to the possible extent, At the same time, the optimal problem can be solved by transforming the behaviour co-nstraints into the boundary ones, Hence, both the method and the programming of optimal dynamic design are simplified and the times of re-analyses are reduced, The theoretical evidence in which the same eigenvalue does not appear as be-fore (so-called the duplicate eigenvalue) during the course of optimality after setting unacceptable band of avoided variable under certain conditions is given and some conditions in which no duplicate eigenvalues appear are also shown in this paper, Following the above method, a practical example of aero engine rotor optimal dynamic design with 25 design variables is given. The optimality value can be achieved by nonlinear programming combined with the method of perturbation converse solution. The times of re-analyses are 5-6. In addition, the authors have made the optimal dynamic design of centrifugal pump. The times of re-analyses are 3-5. This method can also be extended to the optimal dynamic structural design.