Analysis and design of nonlinear resonances via singularity theory
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Peer-reviewed
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Abstract
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.
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Keywords
nonlinear frequency response, detached resonance curve, singularity theory
Journal Title
Journal of Sound and Vibration
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0022-460X
1095-8568
1095-8568
Volume Title
392
Publisher
Elsevier
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Sponsorship
European Research Council (670645)
G. Habib would like to acknowledge the financial support of the Belgian National Science Foundation FRS-FNRS (PDR T.0007.15). The research leading to these results has received funding from the European Research Council under the Advanced ERC Grant Agreement Switchlet n.670645.