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
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