Forces in Mechanics (Oct 2021)
Radiation force of stationary elastic compressional and shear plane waves on a cylinder encased in a linear elastic solid
Abstract
The assembly of acoustically-engineered composite (meta)materials rely on the acousto-elastic radiation force of stationary waves to trap solid particles and form a stable structure. Accurate modeling of the time-averaged force on a particle is needed for experimental design purposes and basic physical understanding of the trapping effect and particle clustering. This work presents a rigorous formalism based on the integration of the time-averaged radial power flow density to derive analytically and calculate numerically the acousto-elastic radiation force induced by compressional (P) and shear (S) plane standing waves incident upon a circular elastic cylinder embedded in a linear lossless solid. Initially, the elastic scattering by the cylinder is determined and then used to derive the acousto-elastic radiation force. Particular emphasis is made on the contributions of elastic mode preservation (P → P, S → S) as well as mode conversion (P → S, S → P) to the radiation force of standing waves. Numerical computations for the dimensionless radiation force efficiency and its components demonstrate the importance of compressional-to-shear and shear-to-compressional mode conversions in scattering that occur in linear elastic media. The analytical formalism and exact solutions of the radiation force can be used to validate numerical methods and the results of the simulations can be utilized a priori in optimizing and designing acousto-elastic radiation force experiments involving standing waves and particle assembly in materials science, elasticity imaging methods, activation of implantable devices, non-destructive evaluation and other related applications.
