Trapping and absorption of sound waves II a sphere covered with a porous layer

Abstract

The acoustic power far away from a sphere covered by a layer of poroelastic medium is compared to that associated with a bare sphere. The effects of a layer of poroelastic medium on the radiation of sound generated by the surface vibration of a sphere, as well as the scattering of an incident plane wave by a stationary sphere, are analyzed. The theory of linear acoustic waves is used in the exterior homogeneous fluid. Biot's theory of poroelasticity is applied to analyze the sound propagation inside the porous layer. The momentum equations for the solid and for the fluid in the porous layer are transformed into three vectorial Helmholtz equations, which enable us to use the method of separation of variables. The results of our study indicate that there is a coupling effect among the two longitudinal waves and one rotational wave. However, when the sphere radius r b is very large or when the frequency ω is very high, the two longitudinal waves are decoupled asymptotically from the rotational wave. By using the material properties for aluminum and hard rubber, the present results show that a more penetrable and rather stiff porous material is very effective in reducing the scattering of acoustic power.