Sensitivity analysis of the eigenvalue problem for general dynamic systems with application to bridge deck flutter

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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.
Original languageEnglish
Pages (from-to)675-682
Number of pages8
JournalJournal of Engineering Mechanics
Volume138
Issue number6
Early online date14 Dec 2011
DOIs
Publication statusPublished - Jun 2012

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Bridge decks
Eigenvalues and eigenfunctions
Sensitivity analysis
Dynamical systems
Aerodynamics
Iterative methods
Systems engineering
Time delay
Aircraft
Mathematical models
Soils
Fluids

Keywords

  • aerodynamics
  • bridges
  • dynamics
  • eigenvalue problem
  • eigenvalues
  • flutter
  • modal analysis
  • sensitivity analysis

Cite this

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title = "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.",
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AB - 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.

KW - aerodynamics

KW - bridges

KW - dynamics

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KW - flutter

KW - modal analysis

KW - sensitivity analysis

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