Analysis and design of nonlinear resonances via singularity theory

Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity theory with one distinguished parameter. While tracking bifurca...

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Bibliographic Details
Published in:Journal of sound and vibration 2017-03, Vol.392, p.295-306
Main Authors: Cirillo, G.I., Habib, G., Kerschen, G., Sepulchre, R.
Format: Article
Language:English
Subjects:
Bifurcation theory
Continuation methods
Detached resonance curve
Mechanical systems
Nonlinear analysis
Nonlinear frequency response
Nonlinear systems
Parameters
Qualitative research
Singularities
Singularity theory
Tracking
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Summary:Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity theory with one distinguished parameter. While tracking bifurcations reveals the qualitative changes in the behaviour, tracking singularities reveals how structural changes are themselves organised in parameter space. The complementarity of that information is demonstrated in the analysis of detached resonance curves in a two-degree-of-freedom system.
ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2016.12.044