NONLINEAR NORMAL MODES AND THEIR APPLICATION IN STRUCTURAL DYNAMICS

Recent progress in the area of nonlinear modal analysis for structural systems is reported. Systematic methods are developed for generating minimally sized reduced‐order models that accurately describe the vibrations of large‐scale nonlinear engineering structures. The general approach makes use of...

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Bibliographic Details
Published inMathematical Problems in Engineering Vol. 2006; no. 1; pp. 10 - 24
Main Authors Pierre, Christophe, Jiang, Dongying, Shaw, Steven
Format Journal Article
LanguageEnglish
Published Hindawi Limiteds 01.01.2006
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Summary:Recent progress in the area of nonlinear modal analysis for structural systems is reported. Systematic methods are developed for generating minimally sized reduced‐order models that accurately describe the vibrations of large‐scale nonlinear engineering structures. The general approach makes use of nonlinear normal modes that are defined in terms of invariant manifolds in the phase space of the system model. An efficient Galerkin projection method is developed, which allows for the construction of nonlinear modes that are accurate out to large amplitudes of vibration. This approach is successfully extended to the generation of nonlinear modes for systems that are internally resonant and for systems subject to external excitation. The effectiveness of the Galerkin‐based construction of the nonlinear normal modes is also demonstrated for a realistic model of a rotating beam.
ISSN:1024-123X
1563-5147
DOI:10.1155/MPE/2006/10847