New model correcting method for quadratic eigenvalue problems using symmetric eigenstructure assignment

Finite element model correction of quadratic eigenvalue problems (QEPs) using a symmetric eigenstructure assignment technique was proposed by Zimmerman and Widengren (Zimmerman, D., and Widengren, M., "Correcting Finite Element Models Using a Symmetric Eigenstructure Assignment Technique" AIAA Journal, Vol. 28, No. 9, 1990, pp. 1670-1676) and 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. Slightly different from the cost function proposed by Zimmerman and Widengren, based on the penalty function given by Friswell et al. (Friswell, M. I., Inman, D. J., and Pilkey, D. F., "Direct Updating of Damping and Stiffness Matrices," AIAA Journal, Vol. 36, No. 3, 1998, pp. 491-493), a cost function is considered that which measures the distance between the analytical and corrected models in a least-squares sense. An efficient algorithm is developed to solve the corresponding optimization problem. The resulting matrices obtained by the new method are necessary and sufficient to the optimization problem. Furthermore, the computational cost of the proposed algorithm requires only O(nm(2)) floating-point operations, where n is the size of coefficient matrices of the QEP and in is the number of the measured modes. The numerical results show that the new method is reliable and attractive.