Modal impedances for a spherical source in a fluid-filled spherical cavity embedded within a fluid-infiltrated elastic porous medium

Abstract

Modal acoustic radiation impedance load on a spherical source vibrating with an arbitrary, axisymmetric, time harmonic velocity distribution, while positioned concentrically within a fluid sphere which is embedded in an infinite fluid-saturated poroelastic medium, is computed. This configuration, which is a realistic idealization of sound projector (transducer) freely suspended in a fluid-filled spherical cavity within a permeable surrounding formation, is of practical importance with a multitude of possible applications in seismo-acoustics and noise control engineering. The formulation utilizes Biot theory of sound propagation in elastic porous media along with the appropriate wave field expansions and the pertinent boundary conditions to determine the resistive and reactive components of model radiation impedances. Numerical example for spherical surface excited in vibrational modes of various order (i.e., monopole, dipole, quadrupole, and multipole like radiators) immersed in a water-filled cavity which is embedded within a water-saturated sandstone surrounding formation is presented. Several limiting cases are discussed. Effects of porosity, frame stiffness, source size and interface permeability condition on the impedance values are presented and discussed. The presented formulation is equally adequate for situations in which the surrounding formation consists of fibrous materials, as in noise control engineering applications.