Analysis and design of nonlinear resonances via singularity theory
Journal of Sound and Vibration
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Cirillo, g., Habib, G., Kerschen, G., & Sepulchre, R. (2017). Analysis and design of nonlinear resonances via singularity theory. Journal of Sound and Vibration, 392 295-306. https://doi.org/10.1016/j.jsv.2016.12.044
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.
nonlinear frequency response, detached resonance curve, singularity theory
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.
ECH2020 EUROPEAN RESEARCH COUNCIL (ERC) (670645)
External DOI: https://doi.org/10.1016/j.jsv.2016.12.044
This record's URL: https://www.repository.cam.ac.uk/handle/1810/263116