Isolated resonances and nonlinear damping

2017/07/12 by Giuseppe Habib, Habib, Giuseppe, Giuseppe Ilario Cirillo +3 · 1 citation
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #math.DS #nlin.CD

paper · pdf · doi:10.48550/arxiv.1707.03561

Author preprint version - manuscript under review

arxiv created 2017/09/19 · arxiv updated 2017/09/20

Abstract

We analyze isolated resonance curves (IRCs) in a single-degree-of-freedom system with nonlinear damping. The adopted procedure exploits singularity theory in conjunction with the harmonic balance method. The analysis unveils 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.

Cited by

• Complex dynamics and route to quasiperiodic synchronization in non-isochronous directed Stuart-Landau triads

Related

• Three types of nonlinear resonances
• The transient route to resonance
• Beyond the Linear Damping Model for Mechanical Harmonic Oscillators
• Modal interactions between a linear oscillator and a nonlinear absorber: multiscale energy transfers
• Enhancing nonlinear damping by parametric-direct internal resonance