求解结构动力逆问题时参数敏感性分析方法

 敏感性分析在求解结构动力逆问题、自动控制、故障诊断、网络设计、工程测量等方面都有重要用途,它也是结构优化设计方法的基础。为使结构具有事先给定的振频和（或）振型而对它进行振动设计或动力修改时,首先就应当寻求其敏感元件或敏感位置,以避免遗漏一些满足要求的结构布局。

SENSITIVITY ANALYSIS OF PARAMETERS IN SOLVING INVERSE PROBLEM OF STRUCTURAL DYNAMICS

A sensitivity analysis method of parameters in solving the inverse problem of structural dynamics is presented on the basis of the perturbation theory. By introducing a set of variable parameters in the structure, the derivatives of structural natural frequencies and/or modes with respect to these parameters are obtained so as to determine the sensitive elements or locations of the structure. In the degenerated case with multiple eigenvalues, the sensitivities of the natural frequencies are obtained by means of puiseux series and considered as the eigenvalues of the matrix. The method is very succinct and able to consider the degenerated case. It is easy to implement the method into the program and to realize the automatization of dynamic design for the structure. So it is suitable especially for engineering practice. This method has been applied to the vibration design of several beam frame structures in the aeronautical engineering. Its success is verified by experimental data,