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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00814435
Contributor : Claude-Henri Lamarque <>
Submitted on : Wednesday, April 17, 2013 - 10:34:31 AM
Last modification on : Tuesday, September 8, 2020 - 6:28:05 PM

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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, Elsevier, 1991, 149 (3), pp.429-459. ⟨10.1016/0022-460X(91)90446-Q⟩. ⟨hal-00814435⟩

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