Diffraction of sound by a poroelastic cylindrical absorber near an impedance plane

Acoustic scattering from an infinitely long fluid-saturated porous elastic circular cylinder located near a planar boundary with locally varying surface impedance is studied. The formulation utilizes the novel features of Biot dynamic theory of poroelasticity, the appropriate wave field expansions, the classical method of images and the translational addition theorem for cylindrical wave functions along with a simple local surface reaction model involving a complex amplitude wave reflection coefficient applied to develop a closed-form solution in the form of infinite series. The analytical results are illustrated with a numerical example in which a cylindrical plastic foam absorber is located near a layer of foam material set on an impervious rigid wall. The numerical results reveal the important effects of incident wave frequency, angle of incidence, interface local surface reaction, cylinder poroelasticity and position on the acoustic field quantities. The proposed model can lead to a better understanding of acoustic scattering from two-dimensional near-interface porous absorbers or targets which are commonly encountered problems in outdoor acoustics, noise control engineering, and ocean engineering. The presented solution could eventually be used to validate those found by numerical approximation techniques.