Vibro-Impact NES: Nonlinear Mode Approximation Using the Multiple Scales Method

The aim of the paper is to derive a closed-form approximation for a nonlinear mode of a system with a vibro-impact nonlinear energy sink. Hereto, the multiple scales method is used to analyze the dynamic behavior of a linear oscillator coupled with a vibro-impact nonlinear energy sink (VI NES). The steady-state response in the vicinity of 1:1 resonance is approximated. The resonance frequency of the examined nonlinear system for different excitation levels is estimated and the corresponding backbone curve is identified. The theoretical findings agree with the simulation results and represent a possible new approach for system identification.