Sound scattering by rough elongated elastic objects. I: Means of scattered field

Abstract

By use of the recently published deformed cylinder formulation [T. K. Stanton, J. Acoust. Soc. Am. 86, 691–705 (1989)], the scattered field due to rough elongated dense elastic objects is derived. The (one-dimensional) roughness is characterized by axial variations of radius. Explicit expressions are derived describing both the mean and mean square of the stochastic scattered field for the rough straight finite length cylinder (broadside incidence) for both ka≪1 and ka≫1 (k is the acoustic wave number and a is the radius) while only the mean is calculated for the prolate spheroid, uniformly bent finite cylinder, and infinitely long cylinder for ka≫1 (again, all broadside incidence). The modal-series-based solution is used in the ka≪1 case as the modal solution simplifies to the sum of two terms (monopole and dipole-like terms). For ka≫1, a more convenient approximate ‘‘ray’’ solution is used in place of the modal series solution. The results show that (1) when ka≪1 the roughness-induced variations of the mean and mean-square scattered fields due to the rough straight finite cylinder depend on the roughness, but are independent of frequency—an effect that has no counterpart in the area of scattering by rough planar interfaces. (2) When ka≫1 the mean specular (geometrically reflected) and Rayleigh surface elastic waves of the scattered field of each object are attenuated due to the roughness and their variations are dependent upon the frequency. In addition, the (roughness-induced) attenuation of the Rayleigh wave depends on the number of times the wave has circumnavigated the object. The mean-square values for the straight finite cylinder are attenuated in a similar manner with the additional dependence upon the correlation distance of the surface.