Prediction of isolated resonance curves using nonlinear normal modes

Isolated resonance curves are separate from the main nonlinear forced-response branch, so they can easily be missed by a continuation algorithm and the resonant re-sponse might be underpredicted. The present work explores the connection between these isolated resonances and the nonlinear normal modes of the system and adapts an energy balance criterion to connect the two. This approach provides new insights into the occurrence of isolated resonances as well as a method to find an initial guess to compute the isolated resonance curve using numerical continuation. The concepts are illustrated on a finite element model of a cantilever beam with a nonlinear spring at its tip. This system presents jumps in both frequency and amplitude in its response to a swept sinusoidal excitation. The jumps are found to be the result of a modal interaction that cre-ates an isolated resonance curve that eventually merges with the main resonance branch as the excitation force increases. Excellent insight into the observed dynamics is provided with the NNM theory, which supports that NNMs can also be a useful tool for predicting isolated resonance curves and other behaviors in the damped, forced response.