Theoretical calculation of the modulated acoustic radiation force on spheres and cylinders in a standing plane wave-field

The acoustic radiation force on objects is the result of nonlinear properties of wave propagation in continuous media. The acoustic radiation force is known to be static for a continuous wave and is used for many applications. This force can also be dynamic (oscillatory) if the incident sound wave-field is modulated (slow time-variations). The purpose of the present paper is to develop the theory for the dynamic radiation force on spheres and cylinders immersed in ideal fluids and placed in a plane standing wave-field. It is assumed that the amplitude-modulated field is produced by dual-frequency plane wave beams propagating along the same direction. Analytical solutions and equations for the dynamic components of the force are derived. Explicit numerical calculations are presented for elastic spheres and cylinders, and rigid and fluid spheres, as well as air bubbles in water. The equations provide analytical radiation force dependencies on the acoustic field and medium parameters. Results show a new dynamic effect in the radiation force functions' curves that results in the splitting of the resonance peaks as long as the modulation frequency increases. It is shown that the radiation force has slow time variations and cannot be treated as a steady-state phenomenon.