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Article Dans Une Revue Journal of Sound and Vibration Année : 1991

Analysis of non-linear dynamical systems by the normal form theory

Louis Jézéquel
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Résumé

A method is proposed for calculating the periodic solutions of non-linear mechanical systems with analytical non-linearities. The Jordan normalization procedure for the case of non-linear autonomous systems is described and generalized to dampened harmonically excited oscillators. Non-linear modes for Hamiltonian systems are introduced; normal forms simplify the analysis of bifurcation. It is shown how to extend, the modal synthesis procedure: the proposed non-linear modes obtained from free vibrations are used to construct a superposition technique to describe the forced response of harmonically excited systems. These results are tested for one- and two-degrees-of-freedom systems with cubic non-linearities. The results are compared with expressions obtained by classical analytical methods (averaging or multiple scales methods) or Runge-Kutta numerical methods.

Dates et versions

hal-00814435 , version 1 (17-04-2013)

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Louis Jézéquel, Claude-Henri Lamarque. Analysis of non-linear dynamical systems by the normal form theory. Journal of Sound and Vibration, 1991, 149 (3), pp.429-459. ⟨10.1016/0022-460X(91)90446-Q⟩. ⟨hal-00814435⟩
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