Non-axisymmetric Acoustic Radiation from a Transversely Oscillating Rigid Sphere above a Rigid/Compliant Planar Boundary

Harmonic acoustic radiation from a transversely oscillating rigid sphere within a fluid halfspace, while its polar axis is oriented either normal or parallel to the rigid/compliant halfspace boundary, is studied using the classical method of separation of variables. The translational addition theorem for spherical wave functions is initially employed to analyze the non-axisymmetric acoustic coupling between a pair of arbitrarily positioned, axisymmetric, finite-sized spherical sources undergoing harmonic modal surface vibrations in an unbounded acoustic medium. Subsequently, the method of images is used to efficiently take the presence of the rigid/compliant boundary into account. The analytical results are illustrated with numerical examples in which the spherical source, vibrating in the horizontal-dipole and vertical-dipole modes, is positioned near the rigid (compliant) boundary of a water-filled acoustic halfspace. Subsequently, the basic acoustic field quantities such as the modal acoustic radiation impedance load and the radiation intensity distribution are evaluated for representative values of the parameters characterizing the system.