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The use of normal forms for analysing nonlinear mechanical vibrations.
Neild, Simon A; Champneys, Alan R; Wagg, David J; Hill, Thomas L; Cammarano, Andrea.
Afiliação
  • Neild SA; Faculty of Engineering, University of Bristol, Bristol BS8 1TR, UK simon.neild@bristol.ac.uk.
  • Champneys AR; Faculty of Engineering, University of Bristol, Bristol BS8 1TR, UK.
  • Wagg DJ; Department of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD, UK.
  • Hill TL; Faculty of Engineering, University of Bristol, Bristol BS8 1TR, UK.
  • Cammarano A; Faculty of Engineering, University of Bristol, Bristol BS8 1TR, UK.
Philos Trans A Math Phys Eng Sci ; 373(2051)2015 Sep 28.
Article em En | MEDLINE | ID: mdl-26303917
A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent variant of the normal form method, that respects the specific structure of such models, is recalled. It is shown how this method can be placed within the context of the general theory of normal forms provided the damping and forcing terms are treated as unfolding parameters. The approach is contrasted to the alternative theory of nonlinear normal modes (NNMs) which is argued to be problematic in the presence of damping. The efficacy of the normal form method is illustrated on a model of the vibration of a taut cable, which is geometrically nonlinear. It is shown how the method is able to accurately predict NNM shapes and their bifurcations.
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Texto completo: 1 Coleções: 01-internacional Base de dados: MEDLINE Tipo de estudo: Prognostic_studies Idioma: En Ano de publicação: 2015 Tipo de documento: Article

Texto completo: 1 Coleções: 01-internacional Base de dados: MEDLINE Tipo de estudo: Prognostic_studies Idioma: En Ano de publicação: 2015 Tipo de documento: Article