The harmonic balance method for bifurcation analysis of nonlinear mechanical systems

Detroux, Thibaut; Renson, Ludovic; Masset, Luc; Kerschen, Gaëtan

doi:10.1007/978-3-319-15221-9_5

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The harmonic balance method for bifurcation analysis of nonlinear mechanical systems

Detroux, Thibaut; Renson, Ludovic; Masset, Luc et al.

2015 • In Proceedings of the International Modal Analysis Conference (IMAC) XXXIII

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https://hdl.handle.net/2268/173556

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10.1007/978-3-319-15221-9_5

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Keywords :

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

Abstract :

[en] 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.

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

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

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

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

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

Language :

English

Title :

The harmonic balance method for bifurcation analysis of nonlinear mechanical systems

Publication date :

2015

Event name :

SEM IMAC XXXIII A Conference and Exposition on Structural Dynamics

Event organizer :

Society for Experimental Mechanics

Event place :

Orlando, Florida, United States

Event date :

2 - 5 February 2015

Audience :

International

Main work title :

Proceedings of the International Modal Analysis Conference (IMAC) XXXIII

European Projects :

FP7 - 307265 - NOVIB - The Nonlinear Tuned Vibration Absorber

Funders :

EU - European Union [BE]

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