Nonlinear normal modes, modal interactions and isolated resonance curves

TL;DR

This paper investigates the relationship between nonlinear normal modes and isolated resonance curves in nonlinear systems, using energy balancing and a cantilever beam example to analyze excitation amplitudes and response behaviors.

Contribution

It introduces a method to connect nonlinear normal modes with isolated resonance curves in damped systems, enhancing understanding of nonlinear dynamic responses.

Findings

Isolated resonance curves can be predicted from nonlinear normal modes.

Energy balancing effectively estimates excitation amplitudes for specific modes.

Response analysis reveals practical implications for nonlinear system excitation.

Abstract

The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system. To this end, an energy balancing technique is used to predict the amplitude of the harmonic forcing that is necessary to excite a specific nonlinear normal mode. A cantilever beam with a nonlinear spring at its tip serves to illustrate the developments. The practical implications of isolated resonance curves are also discussed by computing the beam response to sine sweep excitations of increasing amplitudes.