Isolated resonances and nonlinear damping

TL;DR

This paper investigates isolated resonance curves in nonlinear damping systems, revealing how the damping force's topology influences their emergence and merging through singularity theory and harmonic balance analysis.

Contribution

It introduces a novel analysis linking damping force topology to IRC behavior using singularity theory and harmonic balance methods.

Findings

Extremas and zeros of damping force relate to IRC appearance and merging.

A geometrical connection between damping force topology and IRCs is established.

The method provides insights into nonlinear damping effects on resonance curves.

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.