Theoretical investigation on resonance characteristics of a vapor bubble based on Laplace transform method

Abstract

In the present paper, resonance characteristics of the vapor bubble oscillating in an acoustic field are investigated analytically. The analytical solution of the non-dimensional perturbation of the instantaneous bubble radius during the transient process in the initial oscillation stage is explicitly obtained and physically analyzed at the resonance situation based on the Laplace transform method. And the typical oscillation behaviors obtained from the analytical solution are thoroughly exhibited and analyzed in the time and frequency domains. In addition, the corresponding oscillation behaviors at the non-resonance situation are also investigated for the purpose of comparisons. Through our investigation, several essential conclusions can be drawn as follows: (1) The analytical solution of the non-dimensional perturbation of the instantaneous bubble radius can be divided into four terms according to the physical meaning. Among them, it is the term related to the acoustic field that causes the progressively violent bubble oscillation. (2) The vapor bubble with a smaller equilibrium radius could respond faster and more significantly to the acoustic field during the oscillation. (3) The bubble oscillation characteristics always exhibit significant differences at the resonance and non-resonance situations in both the time and frequency domains, even if the difference between the natural frequency of the oscillating vapor bubble and the angular frequency of the acoustic field is greatly small.

Keywords

• Vapor bubble oscillation
• Resonance characteristics
• Laplace transform