Vibrational resonance in vibro-impact oscillator through fast harmonic excitation

TL;DR

This paper investigates vibrational resonance in a non-smooth Van der Pol-Duffing oscillator with a one-sided barrier, demonstrating that high-frequency harmonic excitation can significantly enhance weak responses through analytical and numerical methods.

Contribution

It extends vibrational resonance concepts to non-smooth systems and provides analytical and numerical insights into the effects of high-frequency excitation.

Findings

High-frequency harmonic excitation enhances weak system responses.

Analytical methods predict resonance phenomena accurately.

Numerical simulations validate the analytical predictions.

Abstract

This study focuses on extending the concept of weak signal enhancement from dynamical systems based on vibrational resonance of nonlinear systems, to non-smooth systems. A Van der Pol- Duffing oscillator with a one-sided barrier, subjected to harmonic excitations, has been considered 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 Blekham 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.