The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems

Harmonic balance; Continuation of periodic solutions; Bifurcation detection and tracking; Floquet exponents; Quasiperiodic oscillations; Detached resonance curves

Abstract :

[en] The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation analysis, i.e., for the detection and tracking of bifurcations of nonlinear systems. To this end, an algorithm that combines the computation of the Floquet exponents with bordering techniques is developed. A new procedure for the tracking of Neimark–Sacker bifurcations that exploits the properties of eigenvalue derivatives is also proposed. The HB method is demonstrated using numerical experiments of a spacecraft structure that possesses a nonlinear vibration isolation device.

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

Detroux, Thibaut ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Renson, Ludovic ; Université de Liège > R&D Direction : Chercheurs ULiège en mobilité

Masset, Luc ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Kerschen, Gaëtan ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Language :

English

Title :

The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems

Publication date :

November 2015

Journal title :

Computer Methods in Applied Mechanics and Engineering

ISSN :

0045-7825

eISSN :

1879-2138

Publisher :

Elsevier, Amsterdam, Netherlands

Volume :

296

Pages :

18-38

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://www.sciencedirect.com/science/article/pii/S0045782515002297

European Projects :

FP7 - 307265 - NOVIB - The Nonlinear Tuned Vibration Absorber

Funders :

UE - Union Européenne
CE - Commission Européenne

Available on ORBi :

since 17 August 2015

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Scopus citations^®

254

Scopus citations^®
without self-citations

214

OpenCitations

154

OpenAlex citations

252

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