Radiation Loading of a Cylindrical Source in a Fluid-Filled Cylindrical Cavity Embedded Within a Fluid-Saturated Poroelastic Medium

Abstract

Radiation loading on a vibrating structure is best described through its radiation impedance. In the present work the modal acoustic radiation impedance load on an infinitely long cylindrical source harmonically excited in circumferentially periodic (axially independent) spatial pattern, while positioned concentrically within a fluid cylinder, which is embedded in a fluid-saturated unbounded elastic porous medium, is computed. This configuration, which is a realistic idealization of an acoustic logging tool suspended in a fluid-filled borehole within a permeable surrounding formation (White, J. E., 1983, Underground Sound Application of Seismic Waves, Elsevier, Amsterdam, Fig. 5.29, p. 183), is of practical importance with a multitude of possible applications in seismo-acoustics and noise control engineering. The formulation utilizes the Biot phenomenological model to represent the behavior of the sound in the porous, fluid-saturated, macroscopically homogeneous and isotropic surrounding medium. Employing the appropriate wave-harmonic field expansions and the pertinent boundary conditions for the given boundary configuration, a closed-form solution in the form of an infinite series is developed and the resistive and reactive components of modal radiation impedances are determined. A numerical example for a cylindrical surface excited in vibrational modes of various order, immersed in a water-filled cavity which is embedded within a water-saturated Ridgefield sandstone environment, is presented and several limiting cases are examined. Effects of porosity, frame stiffness, source size, and the interface permeability condition on the impedance values are presented and discussed.