Full numerical solution for the far-field and near-field scattering from a fluid-loaded elastic plate with distributed mass or stiffness inhomogeneity

Abstract

The scattering of a plane acoustic wave by a fluid-loaded thin elastic plate of infinite extent with a distributed mass or stiffness inhomogeneity is investigated. This paper is a follow up to previous work done by the same authors on the scattering from a fluid-loaded plate with a distributed mass inhomogeneity. In this paper both stiffness and mass distributed inhomogeneities are considered and a complete description of the full numerical solution is presented. Furthermore, both near-field and far-field scattering results are presented in this paper. The presence of the distributed inhomogeneity modifies the wave number transform of the equation of motion of the fluid-loaded plate to a Fredholm integral equation. This integral equation has singularities at the roots of the dispersion equation. To obtain a complete numerical solution of the Fredholm integral equation, a singularity subtraction technique is used, which is similar in essence to the hybrid analytic/numerical approach for the solution of the scattering from a fluid-loaded elastic plate [J. Acoust. Soc. Am. 95, 1998–2005 (1994)]. The solution to the resulting Fredholm integral equation of the second kind is obtained using the Nyström approximation. The results for the far-field scattering are for an oblique angle of incidence and for monostatic scattering. The results show that mass distributed inhomogeneities are stronger scatterers than distributed stiffness inhomogeneities for frequencies below the critical frequency of the plate. Above the critical frequency, both types of inhomogeneities have similar scattering strengths. Also included are results for different types of inhomogeneity distributions. This work was sponsored by ONR.