New Mode Tracking Methods in Aeroelastic Analysis

Within the context of analysis of finite element models, a methodology is developed for the tracking of complex eigenvalues and eigenvectors through changes in aeroelastic eigenvalue problems. The goal is to eliminate difficulties caused by mode switching (i.e., frequency crossing). Two new methods for mode tracking are presented and compared with an existing method. The first new method, the complex 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 new method is the complex cross-orthogonality check method which uses mass biorthogonality of the left and right eigenvectors to re-establish correspondence after a standard reanalysis. Applications of mode tracking technology are presented in V-g and/?^fc subsonic aeroelastic analyses. Each application procedure is outlined and examples are given. Recommendations are made based on method ease of use and robustness in the example problems.