Nonlinear Dynamics

, Volume 93, Issue 3, pp 979–994 | Cite as

Isolated resonances and nonlinear damping

  • Giuseppe Habib
  • Giuseppe I. Cirillo
  • Gaetan Kerschen
Original Paper


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.


Isolated resonance curves Isola Singularity theory Nonlinear damping 


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied MechanicsBudapest University of Technology and EconomicsBudapestHungary
  2. 2.Department of EngineeringUniversity of CambridgeCambridgeUK
  3. 3.Department of Aerospace and Mechanical EngineeringUniversity of LiegeLiègeBelgium

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