Bifurcation analysis of a spacecraft structure using the harmonic balance method

T. Detroux; L. Renson; L. Masset; J. P. Nöel; G. Kerschen

doi:10.1115/DETC201546259

Bifurcation analysis of a spacecraft structure using the harmonic balance method

T. Detroux^*, L. Renson, L. Masset, J. P. Nöel, G. Kerschen

^*Corresponding author for this work

Department of Engineering Mathematics

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

Abstract

The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear models. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. The present paper proposes to extend the method to the detection and tracking of bifurcations in the codimension-2 system parameters space. To validate the methodology, the forced response of a real spacecraft is examined. The paper first provides some numerical evidence of the presence of quasiperiodic oscillations and isolated solutions. It then demonstrates how the tracking of Neimark-Sacker and fold bifurcations can help get a deeper understanding of these attractors.

Original language	English
Title of host publication	27th Conference on Mechanical Vibration and Noise
Publisher	American Society of Mechanical Engineers (ASME)
Volume	8
DOIs	https://doi.org/10.1115/DETC201546259
Publication status	Published - 2015
Event	Conference on Mechanical Vibration and Noise - Boston, United States Duration: 2 Aug 2015 → 5 Aug 2015 Conference number: 27th

Conference

Conference	Conference on Mechanical Vibration and Noise
Abbreviated title	VIB
Country/Territory	United States
City	Boston
Period	2/08/15 → 5/08/15

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@inproceedings{ccdbd6aaf62447f6a1e142160e88306a,

title = "Bifurcation analysis of a spacecraft structure using the harmonic balance method",

abstract = "The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear models. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. The present paper proposes to extend the method to the detection and tracking of bifurcations in the codimension-2 system parameters space. To validate the methodology, the forced response of a real spacecraft is examined. The paper first provides some numerical evidence of the presence of quasiperiodic oscillations and isolated solutions. It then demonstrates how the tracking of Neimark-Sacker and fold bifurcations can help get a deeper understanding of these attractors.",

author = "T. Detroux and L. Renson and L. Masset and N{\"o}el, {J. P.} and G. Kerschen",

year = "2015",

doi = "10.1115/DETC201546259",

language = "English",

volume = "8",

booktitle = "27th Conference on Mechanical Vibration and Noise",

publisher = "American Society of Mechanical Engineers (ASME)",

address = "United States",

note = "Conference on Mechanical Vibration and Noise, VIB ; Conference date: 02-08-2015 Through 05-08-2015",

}

Detroux, T, Renson, L, Masset, L, Nöel, JP & Kerschen, G 2015, Bifurcation analysis of a spacecraft structure using the harmonic balance method. in 27th Conference on Mechanical Vibration and Noise. vol. 8, American Society of Mechanical Engineers (ASME), Conference on Mechanical Vibration and Noise, Boston, Massachusetts, United States, 2/08/15. https://doi.org/10.1115/DETC201546259

TY - GEN

T1 - Bifurcation analysis of a spacecraft structure using the harmonic balance method

AU - Detroux, T.

AU - Renson, L.

AU - Masset, L.

AU - Nöel, J. P.

AU - Kerschen, G.

N1 - Conference code: 27th

PY - 2015

Y1 - 2015

N2 - The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear models. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. The present paper proposes to extend the method to the detection and tracking of bifurcations in the codimension-2 system parameters space. To validate the methodology, the forced response of a real spacecraft is examined. The paper first provides some numerical evidence of the presence of quasiperiodic oscillations and isolated solutions. It then demonstrates how the tracking of Neimark-Sacker and fold bifurcations can help get a deeper understanding of these attractors.

AB - The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear models. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. The present paper proposes to extend the method to the detection and tracking of bifurcations in the codimension-2 system parameters space. To validate the methodology, the forced response of a real spacecraft is examined. The paper first provides some numerical evidence of the presence of quasiperiodic oscillations and isolated solutions. It then demonstrates how the tracking of Neimark-Sacker and fold bifurcations can help get a deeper understanding of these attractors.

UR - http://www.scopus.com/inward/record.url?scp=84979032214&partnerID=8YFLogxK

U2 - 10.1115/DETC201546259

DO - 10.1115/DETC201546259

M3 - Conference Contribution (Conference Proceeding)

AN - SCOPUS:84979032214

VL - 8

BT - 27th Conference on Mechanical Vibration and Noise

PB - American Society of Mechanical Engineers (ASME)

T2 - Conference on Mechanical Vibration and Noise

Y2 - 2 August 2015 through 5 August 2015

ER -

Bifurcation analysis of a spacecraft structure using the harmonic balance method

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