Sensitivity Analysis of the Eigenvalue Problem for General Dynamic Systems with Application to Bridge Deck Flutter

Abstract

The mathematical models governing the dynamics of various engineering systems, such as airplane wings and bridge decks subjected to aerodynamic forces, mechanical and civil structures interacting with fluid or soil, or systems with time delays, yield transcendental eigenvalue problems. In this work, a general transcendental eigenvalue problem is first formulated and a biorthogonality relationship between eigenvectors is derived. Then, the sensitivities of eigenvalues and eigenvectors with respect to a system parameter are obtained. The method is employed to analyze in detail a transcendental eigenvalue problem arising in the analysis of a bridge deck subjected to aerodynamic forces. The sensitivities of eigenvalues and eigenvectors are successfully used to improve the performance of an iterative method used for solving the eigenvalue problem.