HIGHER-ORDER EIGENPAIR PERTURBATIONS

A matrix method is presented for the exact calculation of large eigenpair perturbations arising from design variable changes. The method is "forward analysis" in the sense that design variable changes are known and eigenpair perturbations are computed. Competing methods for forward analysis include reanalysis and first-order approximate methods. First-order methods are well known for their ability to calculate small eigenpair changes but are inadequate when large changes are required. In this paper, a new method of forward analysis is presented that takes into account all orders of the perturbation expansion. A benchmark cantilever beam will be analyzed with the new method for large perturbations in design variables. The method will be valuable for fast reanalysis and for identification and model correlation studies where sizeable differences exist between a baseline model and an objective model.