Nonlinear dynamics of two coupled bubbles oscillating inside a liquid-filled cavity surrounded by an elastic medium

Abstract

A theory is developed to model the nonlinear dynamics of two coupled bubbles inside a spherical liquid-filled cavity surrounded by an elastic medium. The aim is to study how the conditions of full confinement affect the coupled oscillations of the bubbles. To make the problem amenable to analytical consideration, the bubbles are assumed to be located on a diameter of the cavity, which makes the problem axisymmetric. Equations for the pulsation and translation motion of the bubbles are derived by the Lagrangian formalism. The derived equations are used in numerical simulations. The behavior of two bubbles in a cavity is compared with the behavior of the same bubbles in an unbounded liquid. It is found that both forced and free oscillations of two bubbles in a cavity occur differently than those in an unbounded liquid. In particular, it is shown that the eigenfrequencies of a two-bubble system in a cavity are different from those in an unbounded liquid.