Induced effects of a rigid boundary on a pulsating spherical source

Abstract

This work develops a comprehensive analytical formalism to study the boundary-induced effects on a pulsating spherical radiating source near a rigid planar boundary in an inviscid fluid. Using the modal multipole expansion method, the image method and the translational addition theorem for spherical wave functions, exact closed-form expressions are derived for the dimensionless axial acoustic radiation force function as well as the radiation, amplification and extinction energy efficiency factors. The source-boundary distance and the dimensionless size parameter are especially addressed in the numerical simulations for spherical sources with different vibration modes. It is shown that the axial radiation force is positive or negative, depending on the choice of parameters. Moreover, cases when the extinction acoustic power completely vanishes are predicted theoretically for dipole and quadrupole vibrations, which can be used to achieve acoustic invisibility in acoustic cloaking devices and acoustic stealth technologies. Combination of more than one vibration modes is also investigated to better simulate the acoustic manipulation in practical applications. This work can help us understand the underlying mechanism in manipulating the active spherical radiating sources in a bounded field.