Elastic Wave Scattering at a Cylindrical Discontinuity in a Solid

Abstract

This study deals with the scattering of plane compressional and shear elastic waves incident obliquely on an infinitely long nondissipative cylindrical elastic discontinuity in an isotropic solid.Equations whose solutions are the coefficients in series expressions for the scatteredwaves are derived for the case of scattering at an elasticsolid cylinder embedded in a different solid medium. From these equations are obtained those governing scattering at a fluid‐filled cylindrical bore, and at an empty bore. In general, when a wave of either the compressional or shear type is incident on an elastic discontinuity, scatteredwaves of both types are produced, a process known as “mode conversion.” A simple relation is shown to exist between the two far‐zone distributions‐in‐angle, and between the two scattering cross sections for the waves undergoing mode conversion in the scattering of compressional and normally polarized shear waves incident normally upon either a fluid‐filled or an empty bore. For an empty bore whose diameter was comparable with a wavelength in the solid, computed distributions‐in‐angle for the scattering of normally incident compressional and normally polarized shear waves were verified experimentally. Measurements were also made of the scattering of compressional waves at a fluid‐filled bore in a solid, and of the far‐zone directivity patterns of some compressional and shear wave piezoelectric source crystals radiating into a solid medium.