Transient acoustic radiation from an eccentric sphere

A vigorous semi-analytical model is offered to describe the 3D coupled nonaxisymmetric non-steady acousto-elastodynamic behavior of a submerged solid sphere with an off-center fluid-filled spherical cavity, acted upon by general distributed time-varying mechanical loads at its internal and/or external boundaries. The solid medium is designated by the 3D Navier’s linear elasticity model, while the internal/external ideal compressible fluids are assumed to obey the classical linear acoustic theory. Laplace transformation is applied to the time variable, and the separation of variables technique together with the pertinent fluid/solid interface conditions, the classical orthogonality properties of spherical harmonics, and a modified form of the translational addition theorem for spherical vector wave functions, are utilized to attain the final matrix equations in terms of unknown modal coefficients. Durbin’s Laplace transform inversion algorithm is subsequently applied to compute the pressure/displacement time response histories of water-submerged eccentric and coaxial metallic spheres excited by a couple of external concentrated Ricker-pulse radial excitations. Also, some key characteristics of the transient structure/liquid interaction phenomena with respect to cavity eccentricity are noted based on selected two-dimensional visualizations of the internal/external sound fields. Lastly, the accuracy of numerical simulations is verified by employing a standard FEM software.