Amplitude nonlinear normal modes of piecewise linear systems

Dongying Jiang, Vincent Soumier, Christophe Pierre, Steven W. Shaw

Research output: Contribution to conferencePaperpeer-review

1 Scopus citations

Abstract

A numerical method for constructing nonlinear normal modes for piecewise linear autonomous systems is presented. Based on the concept of invariant manifolds, a Galerkin based approach is applied here to obtain nonlinear normal modes numerically. The accuracy of the constructed nonlinear modes is checked by the comparison of the motion on the invariant manifold to the exact solution, in both time and frequency domains. It is found that the Galerkin based construction approach can represent the invariant manifold accurately over strong nonlinearity regions. Several interesting dynamic characteristics of the nonlinear modal motion are found and compared to those of linear modes. The stability of the nonlinear normal modes of a two-degree of freedom system is investigated using characteristic multipliers and Poincaré maps, and a flip bifurcation is found for both nonlinear modes.

Original languageEnglish
Pages3039-3048
Number of pages10
StatePublished - 2001
Event18th Biennial Conference on Mechanical Vibration and Noise - Pittsburgh, PA, United States
Duration: 9 Sep 200112 Sep 2001

Conference

Conference18th Biennial Conference on Mechanical Vibration and Noise
Country/TerritoryUnited States
CityPittsburgh, PA
Period9/09/0112/09/01

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