Nonlinear normal modes for vibratory systems under periodic excitation

Dongying Jiang, Christophe Pierre, Steven W. Shaw

Research output: Contribution to conferencePaperpeer-review

4 Scopus citations

Abstract

This paper considers the use of numerically constructed invariant manifolds to determine the response of nonlinear vibratory systems that are subjected to periodic excitation. The approach is an extension of the nonlinear normal mode formulation previously developed by the authors for free oscillations, wherein an auxiliary system that models the excitation is used to augment the equations of motion. In this manner, the excitation is simply treated as an additional system state, yielding a system with an extra degree of freedom, whose response is known. A reduced order model for the forced system is then determined by the usual nonlinear normal mode procedure, and an efficient Galerkin-based solution method is used to numerically construct the attendant invariant manifolds. The technique is illustrated by determining the frequency response for a simple two-degree-of-freedom mass-spring system with cubic nonlinearities, and for a discretized beam model with 12 degrees of freedom. The results show that this method provides very accurate responses over a range of frequencies near resonances.

Original languageEnglish
Pages1177-1188
Number of pages12
DOIs
StatePublished - 2003
Event2003 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Chicago, IL, United States
Duration: 2 Sep 20036 Sep 2003

Conference

Conference2003 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Country/TerritoryUnited States
CityChicago, IL
Period2/09/036/09/03

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