Resonance Dynamics in a Double-Well Parametric Quintic Oscillator: Probing Well Depth and Location Dependencies

Abstract

This study explores the influence of the depth and location of minima of a double-well potential on vibrational resonance in a parametric quintic oscillator. The system experiences dual driving forces-a low-frequency component, (f cos ωt), and a high-frequency component, (g cos Ωt). The response of the system manifests in two distinct motions: a slow motion characterized by the frequency ω and a fast motion characterized by the frequency Ω. Utilizing the flow equation approach, we analytically derive the response amplitude a0(ω) from the equation governing the system’s slow motion. By employing an approximate theoretical expression for a0(ω) at low frequencies (ω), we investigate the impact of the depth and location of minima of the double-well potential on vibrational resonance. Modulating the amplitude of the high-frequency force g allows control over the number of resonances based on the depth and location of the wells. Adjusting system parameters through the manipulation of well depth and location enables the achievement of optimal vibrational resonance. Moreover, the alterations induced by these two parameters in the parametrically driven system are found to be more extensive than those observed in the original system. The theoretical results are validated through numerical simulations.