Sensitivity Analysis of the Eigenvalue Problem for General Dynamic Systems with Application to Bridge Deck Flutter
Publication: Journal of Engineering Mechanics
Volume 138, Issue 6
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.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 138 • Issue 6 • June 2012
Pages: 675 - 682
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Nov 14, 2010
Accepted: Dec 12, 2011
Published online: Dec 14, 2011
Published in print: Jun 1, 2012
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