A New Model Correcting Method for Quadratic Eigenvalue Problems Using a Symmetric Eigenstructure Assignment

Finite element model correction of quadratic eigenvalue problems (QEPs) using a symmetric eigenstructure assignment technique is proposed by Zimmerman and Widengren 1989, which incorporates the measured model data into the finite element model to produce an adjusted finite element model on the damping and stiffness matrices that matches the experimental model data, and minimizes the distance between the analytical and corrected models. In this paper, we mainly develop an efficient algorithm to solve the corresponding optimization problem in a least-squares sense. The resulting matrices obtained by the new method are necessary and sufficient to the optimization problem. Furthermore, the proposed algorithm only needs to solve a linear system and totally requires O(nm2) flops, where n is the size of coefficient matrices of the QEP and m is the number of the measured modes. The numerical results show that the new method is reliable and attractive.