Sound radiation from a liquid-filled underwater spherical acoustic lens with an internal eccentric baffled spherical piston

An exact study on reradiation of an acoustic field due to radial/axial vibrations of a baffled spherical piston, while eccentrically positioned within a fluid-filled thin spherical elastic shell, into an external fluid medium is presented. This configuration, which is a realistic idealization of a liquid-filled spherical acoustic lens with focal point inside the lens when used as a sound projector, is of practical importance with multitude of possible applications in ocean engineering and underwater acoustics. The formulation utilizes the appropriate wave field expansions along with the translational addition theorems for spherical wave functions to develop a closed-form solution in form of infinite series. Numerical results reveal that in addition to frequency, cap angle, radiator position (eccentricity), cap surface velocity distribution, and dynamics of the elastic shell can be of significance in sound radiation.