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

T. Detroux; Ludovic Renson; L. Masset; Gaetan Kerschen

doi:10.1016/j.cma.2015.07.017

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

T. Detroux^*, Ludovic Renson, L. Masset, Gaetan Kerschen

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

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.

Original language	English
Pages (from-to)	18-38
Number of pages	21
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	296
Early online date	23 Jul 2015
DOIs	https://doi.org/10.1016/j.cma.2015.07.017
Publication status	Published - 1 Nov 2015

Keywords

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

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10.1016/j.cma.2015.07.017

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at http://www.sciencedirect.com/science/article/pii/S0045782515002297. Please refer to any applicable terms of use of the publisher.
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title = "The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems",

abstract = "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.",

keywords = "Bifurcation detection and tracking, Continuation of periodic solutions, Detached resonance curves, Floquet exponents, Harmonic balance, Quasiperiodic oscillations",

author = "T. Detroux and Ludovic Renson and L. Masset and Gaetan Kerschen",

year = "2015",

month = nov,

day = "1",

doi = "10.1016/j.cma.2015.07.017",

language = "English",

volume = "296",

pages = "18--38",

journal = "Computer Methods in Applied Mechanics and Engineering",

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TY - JOUR

T1 - The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems

AU - Detroux, T.

AU - Renson, Ludovic

AU - Masset, L.

AU - Kerschen, Gaetan

PY - 2015/11/1

Y1 - 2015/11/1

N2 - 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.

AB - 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.

KW - Bifurcation detection and tracking

KW - Continuation of periodic solutions

KW - Detached resonance curves

KW - Floquet exponents

KW - Harmonic balance

KW - Quasiperiodic oscillations

UR - https://www.scopus.com/pages/publications/84939600715

U2 - 10.1016/j.cma.2015.07.017

DO - 10.1016/j.cma.2015.07.017

M3 - Article (Academic Journal)

AN - SCOPUS:84939600715

SN - 0045-7825

VL - 296

SP - 18

EP - 38

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

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

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