Abstract: According to the theories of eigenvalue perturbation and structural matrix perturbation, an inverse perturbation method of optimal dynamic design of mechanical system is put forward by taking advantage of the idea of inverse solution. The method can be combined with mathematical method, criterion method or matrix perturbation method in order to avoid re-analysis as far as possible, and the initiative of the engineers and technicians can be brought into play also. The method is fit to solve the complex optimal dynamic design problems with dynamic behavior constraints while faking finite element method as analysis tool. Several examples are given in the later part of this paper. The method can also be used for the optimal dynamic design of engineering structures.

Key words: Dynamic, Finite element method, Inverse problem, Optimal design, Perturbation