Dynamic Design of Structures Based on Kind of Inverse Generalized Eigenvalue Problem for Matrices

The stiffness matrix and mass matrix are considered as nonlinear functions of certain parameters such as the areas of cross section of the members. In this paper, a method of structural design of dynamic model is presented and the solving criterion is also given. A first, the problem is treated as a kind of inverse generalized eigenvalue problem for matrices dependent on parameters. Then, according to the characteristic of the inverse generalized eigenvalue problem, the calculation for the global matrices can be transformed into calculation for the specified local matrices. The derivatives of eigenvalues and eigenvectors are solved by a mathematical algorithm. Computing efficiency is improved greatly. The numerical example shows the benefit of the presented methodology.