Nonlinear Dynamics

, Volume 41, Issue 1–3, pp 147–169

The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview

  • Gaetan Kerschen
  • Jean-claude Golinval
  • ALEXANDER F. VAKAKIS
  • LAWRENCE A. BERGMAN
Article

Abstract

Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New developments have been proposed in order to examine nonlinear systems, among which the theory based on nonlinear normal modes is indubitably the most appealing. In this paper, a different approach is adopted, and proper orthogonal decomposition is considered. The modes extracted from the decomposition may serve two purposes, namely order reduction by projecting high-dimensional data into a lower-dimensional space and feature extraction by revealing relevant but unexpected structure hidden in the data. The utility of the method for dynamic characterization and order reduction of linear and nonlinear mechanical systems is demonstrated in this study.

Key Words

dynamic characterization order reduction proper orthogonal decomposition 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Gaetan Kerschen
    • 1
    • 5
    • 6
  • Jean-claude Golinval
    • 1
  • ALEXANDER F. VAKAKIS
    • 2
    • 3
  • LAWRENCE A. BERGMAN
    • 4
  1. 1.Department of Materials, Mechanical and Aerospace EngineeringUniversity of LiègeLiègeBelgium
  2. 2.Division of MechanicsNational Technical University of AthensAthensGreece
  3. 3.Department of Mechanical and Industrial Engineering (adjunct), Department of Aerospace Engineering (adjunct)University of Illinois at Urbana-ChampaignIllinoisU.S.A.
  4. 4.Department of Aerospace EngineeringUniversity of Illinois at Urbana-ChampaignIllinoisU.S.A.
  5. 5.Postdoctoral fellowNational Technical University of AthensAthensGreece
  6. 6.University of Illinois at Urbana-ChampaignIllinoisU.S.A.

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