Abstract
The phenomenon of vibrational resonance (VR) has been investigated in a Rayleigh-Plesset oscillator for a gas bubble oscillating in an incompressible liquid while driven by a dual-frequency force consisting of high-frequency, amplitude-modulated, weak, acoustic waves. The complex equation of the Rayleigh-Plesset bubble oscillator model was expressed as the dynamics of a classical particle in a potential well of the Liénard type, thus allowing us to use both numerical and analytic approaches to investigate the occurrence of VR. We provide clear evidence that an acoustically-driven bubble oscillates in a time-dependent single or double-well potential whose properties are determined by the density of the liquid and its surface tension. We show both theoretically and numerically that, besides the VR effect facilitated by the variation of the parameters on which the high-frequency depends, amplitude modulation, the properties of the liquid in which the gas bubble oscillates contribute significantly to the occurrence of VR. In addition, we discuss the observation of multiple resonances and their origin for the double-well case, as well as their connection to the low frequency, weak, acoustic force field.
Highlights
Nonlinear dynamical systems are ubiquitous in nature and they exhibit a diversity of fascinating phenomena
We have examined the oscillations of an acousticallyforced gas bubble in an incompressible liquid, using the Rayleigh-Plesset bubble model
We showed that the bubble oscillation could be expressed as the dynamics of a particle in a time-dependent single or double-well potential whose properties are determined by the density of the liquid and its surface tension
Summary
Nonlinear dynamical systems are ubiquitous in nature and they exhibit a diversity of fascinating phenomena. In the light of the forgoing, we investigate and analyze the VR phenomenon in a model of an amplitude-modulated, acoustically-driven gas bubble in an incompressible liquid which, to the best of our knowledge, has not previously been discussed Bubbles appear in both the life sciences and natural sciences, as well as in technology [43], and their dynamics has received considerable attention in connection with acoustic cavitation [42,43,44] where bubbles are excited by an acoustic sound field mostly consisting of single or dual frequencies.
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