The harmonic balance method for bifurcation analysis of nonlinear mechanical systems

T. Detroux*, L. Renson, L. Masset, G. Kerschen

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

1 Citation (Scopus)
338 Downloads (Pure)

Abstract

Because nowadays structural engineers are willing to use or at least understand nonlinearities instead of simply avoiding them, there is a need for numerical tools performing analysis of nonlinear large-scale structures. Among these techniques, the harmonic balance (HB) method is certainly one of the most commonly used to study finite element models with reasonably complex nonlinearities. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. For this reason, the present paper proposes to extend the method to the detection and tracking of codimension-1 bifurcations in the system parameters space. As an application, the frequency response of a spacecraft is studied, together with two nonlinear phenomena, namely quasiperiodic oscillations and detached resonance curves. This example illustrates how bifurcation tracking using the HB method can be employed as a promising design tool for detecting and eliminating such undesired behaviors.

Original languageEnglish
Title of host publicationDynamic Behavior of Materials
Subtitle of host publicationProceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015
EditorsGaëtan Kerschen
PublisherSpringer, New York, NY
Pages65-82
Number of pages18
Volume1
ISBN (Electronic)9783319152219
ISBN (Print)9783319152202
DOIs
Publication statusPublished - 2016
Event33rd IMAC Conference and Exposition on Structural Dynamics, 2015 - Orlando, FL, United States
Duration: 2 Feb 20155 Feb 2015

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
PublisherSpringer International Publishing
ISSN (Print)2191-5644

Conference

Conference33rd IMAC Conference and Exposition on Structural Dynamics, 2015
CountryUnited States
CityOrlando, FL
Period2/02/155/02/15

Keywords

  • Bifurcation tracking
  • Continuation of periodic solutions
  • Detached resonance curves
  • Harmonic balance method
  • Quasiperiodic oscillations

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