Vibrational resonance in nearly elastic vibro-impact oscillator driven by fast harmonic excitation

Abstract

This study focuses on extending the concept of weak signal enhancement from dynamical systems based on the vibrational resonance of nonlinear systems, to non-smooth systems close to the elastic limit. A Van der Pol- Duffing oscillator with a one-sided barrier, subjected to harmonic excitations, has been considered as an archetypical low order model, whose response is weak. It is shown that the system response can be significantly enhanced by applying an additional harmonic excitation but with much higher frequencies. The reasons for the underlying physics are investigated analytically using multiple-scale analysis and the Blekhman perturbation approach (direct partition motion). The analytical predictions are qualitatively validated using numerical simulations. This approach yields valuable insights into the intricate interplay between fast and slow excitations in non-smooth systems.