Acoustic field effect on encapsulated spherical drop located in liquid filled cylindrical vessel

Abstract

The acoustical problem dealing with the interaction of a plane wave propagating along the liquid-filled cylindrical cavity with an elastic spherical shell filled, in turn, with the compressible liquid is solved. An axisymmetric case is studied. The boundary problem for simultaneous solution of the wave equations describing the motion in the fluid filling the vessel as well as in the fluid contained within the shell together with equations of motion of the thin elastic shell is formulated. The problem statement contains the boundary conditions for both fluid–shell interfaces, the condition at the vessel surface and far-field radiation conditions. The incident wave propagating along the vessel axis is expanded into a normal mode series. In order to meet all boundary conditions, the variable separation method along with the spherical wave function representations in terms of the cylindrical ones and vice versa are used. This approach yields exact solution of the boundary problem and enables one to analyze the scattered fields in the low and medium frequency ranges. The problem is reduced to an infinite system of algebraic equations that is solved by the truncation method. The goal of the study is to determine the interaction features between the shell and the vessel surfaces. Obtained numerical results describe scattered field of pressure and velocity in the neighborhood of the shell as functions of frequency, the internal liquid characteristics, and the elastic characteristics of the shell. It is ascertained, that peculiarities of the resonance behavior of the liquid-filled shell can be essentially amplified by the acoustical interaction with the vessel surface.