Acousto-elastic radiation force on a fluid cylindrical inclusion embedded in a linear elastic medium

Abstract

In the framework of linear elasticity, the longitudinal acousto-elastic time-averaged radiation force exerted on a cylindrical fluid-filled inclusion of arbitrary size embedded in an unbounded elastic matrix is derived based upon the integration of the time-averaged power flow density over a surface enclosing the particle. The cases of compressional and shear plane progressive elastic waves are considered. Mathematical expressions for the longitudinal radiation force efficiencies are derived and cast in exact series expansions in cylindrical coordinates. The elastic scattering solution, which is utilized to derive the acousto-elastic radiation force expressions, is determined. The analytical expressions for the acousto-elastic radiation force clearly show the contributions related to mode conversion P → S for the incident compressional waves, and S → P for shear wave incidence (where P and S denote, respectively, the compressional and shear waves). Another method, based on the extinction energy efficiency and the scattering asymmetry parameter, is shown to provide the same exact expression of the force obtained based upon the power flow density formalism. Computations for the dimensionless radiation force efficiencies and their cross-polarized (P → S and S → P) components demonstrate that mode conversion contributes negatively, positively or neutrally depending on the mass density of the particle, its size, and the properties of the surrounding elastic medium. In addition, elastic resonances are manifested in the acousto-elastic radiation force plots. This analysis provides a rigorous exact formalism using exact partial-waves series to compute the acousto-elastic radiation forces of compressional or shear waves on an elongated cylindrical particle encased in a linear elastic medium. The analytical series expressions and numerical predictions can be used as a priori information in optimizing and designing acousto-elastic radiation force experiments in materials science, elastography, vibro-acoustography, nondestructive evaluation, and the activation/excitation of a fluid cylinder embedded in an elastic medium, to name a few examples. The electromagnetic/optical analogue for materials exhibiting circular dichroism is also noted.