Mode Tracking Issues in Structural Optimization

Within the context of optimization of the structural dynamics properties of finite element models, methodology is developed for the tracking of eigenpairs through changes in the structural eigenvalue problem. The goal is to eliminate difficulties caused by "mode switching" (i.e., frequency crossing). Out of several candidate methods, two methods for mode tracking are successful. The first method, the higher order eigenpair perturbation algorithm, is based on a perturbation expansion of the eigenproblem. It iteratively computes changes in the eigenpairs due to parameter perturbations with the important feature of maintaining the correspondence between the baseline and perturbed eigenpairs. The second method is a cross-orthogonality check method, which uses mass orthogonality to reestablish correspondence after a standard reanalysis. Modified eigenpair extraction routines (Lanczos, subspace iteration, inverse power) were unsuccessful in tracking modes. Applications of mode tracking technology that are presented are frequency-constrained optimization and optimization with mode shape constraints. Each application procedure is outlined and examples are given. Recommendations are made based on method efficiency and robustness in the example problems.