求解结构动力反问题的逆特征值方法

 设计一个结构,使其具有事先给定的频率和（或）振型,这类结构动力反问题有重要的应用和理论价值。本文提出了求解它的逆特征值方法,并给出了数值例子。算例一说明:逆特征值方法的计算精度要比反摄动法高得多。经过实验验证的算例二表明:计算值、目标值和实验值十分吻合。

THE INUERSE EIGENUALUE ALGORIOTHM FOR RESOLUiNG THE INUERSE PROBLEMS OF STRUCTURAL DYNAMICS

Desinging a structure with prescribed vibration frequenc ies and/or modes of vibration is called inverse problem of structural dynamics. It has important value both in practice and theory. In this paper, an inverse eigenvalue method for resolving this problem is presented. The main idea of the method is to consider the inverse problem of structural dynamics as a generalized inverse eigenvalue problem （2.5）^2.7 and build a functional （3.8）. Then this problem is reduced to finding minimum of a qu-ardratic functional subject to constrains. The algorithm uses random numbers to generate the initial value automatically. It is suitable to structural dynamic modifications or of high accuracy and vibration design with reliable convergence. It can be used when frequencies and modes of vibration are given or only the frequencies are given. The orders of desirable frequencies and/or modes of vibration are optional. Possible limitations in design have also been consider. The numerical examples and experiments have showen that the algorithm is wffective. It has been applied to theoretical physics and aeronautical engineering successfully ahd effectively.