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Isolated resonances and nonlinear damping

Abstract

We analyze isolated resonance curves (IRCs) in single-degree-of-freedom systems possessing nonlinear damping. Through the combination of singularity theory and the averaging method, the onset and merging of IRCs, which coincide to isola and simple bifurcation singularities, respectively, can be analytically predicted. Numerical simulations confirm the accuracy of the analytical developments. Another important finding of this paper is that we unveil a geometrical connection between the topology of the damping force and IRCs. Specifically, we demonstrate that extremas and zeros of the damping force correspond to the appearance and merging of IRCs. Considering a damping force possessing several minima and maxima confirms the general validity of the analytical result. It also evidences a very complex scenario for which different IRCs are created, co-exist and then merge together to form a super IRC which eventually merges with the main resonance peak.

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Correspondence to Giuseppe Habib.

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This study was financially supported by the European Union, H2020 Marie Skłodowska-Curie IF 704133 (G. Habib) and ERC Starting Grant NoVib 307265 (G. Kerschen).

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Habib, G., Cirillo, G.I. & Kerschen, G. Isolated resonances and nonlinear damping. Nonlinear Dyn 93, 979–994 (2018). https://doi.org/10.1007/s11071-018-4240-z

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Keywords

  • Isolated resonance curves
  • Isola
  • Singularity theory
  • Nonlinear damping