基于矩阵逆特征值法的结构动力学设计

结构刚度矩阵和质量矩阵是关于设计参数的函数,而且事实上一般是非线性函数.结构动力学设计通常要求结构具有指定的动力特性,结构动力学设计问题可以归纳为一类含设计参数的广义逆特征值问题.首先给出了结构动力学设计问题的数学描述以及相应的求解准则和方法,然后,利用矩阵逆特征值问题的特点,将原来对整体矩阵的计算转化为对特定的局部矩阵的计算,整体矩阵与局部矩阵之间的数学和物理性质有明确的对应关系,既大大降低了计算量,又能保证计算精度.算例证明了本文方法良好的性能.

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.