Delay-induced vibrational resonance in the Rayleigh–Plesset bubble oscillator

Abstract

We examine the impacts of time-delay and phase shift between two acoustic driving forces on vibrational resonance (VR) phenomena in the oscillations of a spherical gas bubble. Using the approximate method of direct separation of the motions, we obtain the equation of slow motion and the response amplitude, and we validate the theoretical predictions with numerical simulations. We find that the response amplitude of the system at the lower frequency varies periodically with respect to the phase shift. When the phase shift consists of an even number of periods, it can be optimized to enhance the system’s response in the relevant parameter space of the high-frequency driving force. In addition to the enhancement of the VR peak by variation of the phase shift, our results show that the time-delay also plays a significant role in the bubble’s response to dual-frequency acoustic driving fields. It and can be exploited either to suppress drastically, or to modulate, the resonance peaks, thereby controlling the resonances. Our analysis shows further that cooperation between the time-delay and the amplitude of the high-frequency component of the acoustic waves can induce multiple resonances. These results could potentially be exploited to control and enhance ultrasonic cleaning processes by varying the time-delay parameter in the presence of phase shifted dual-frequency acoustic waves. Moreover, it could be employed to achieve improved accuracy in ultrasonic biomedical diagnosis and tumour therapy, as well as for targeted delivery of reagents transported within bubbles.