基于Moore-Penrose广义逆的模型修正方法

A model updating method based on Moore-Penrose inverse

结构动力学有限元模型的修正对于结构动特性、动响应乃至动强度的计算都具有重要意义。用矩阵型方法进行模型修正时,由于测试模态数目较少,导致修正过程中的方程欠定,很难求解出满意的修正结果,为此提出了一种新的有限元模型刚度矩阵和质量矩阵的求解方法。从数学的角度出发,以待修正模型的质量矩阵和刚度矩阵作为修正矩阵的估计,同时利用质量矩阵和刚度矩阵的稀疏性和对称性,得到具有较高精度的修正矩阵。以简单的梁和板为例,验证了该求解方法的可行性和有效性。

Updating for dynamic model of a structure is important for calculating of structure dynamic characteristics,responses as well as the dynamic strength.The results after updating with the matrix methods are not well satisfied,as the measured modes available are limited which caused the updating equations underdetemined.A new method to solve these underdetermined equations is proposed.Take the initial stiffness and mass matrices to be updated as estimate of update matrix,and use their sparse and symmetry,the update matrix with high precision is obtaind.Examples of a beam and a plate are presented to demonstrate the feasibility and the validity.