Three dimensional scattering of elastic waves by surface corrosion pits

Abstract

Elastic wave scattering by surface defects like cracks, corrosion induced pits, topographic irregularities, ~:tc., is of interest for ultrasonic nondestructive evaluation and in seismology. Scattering by surface-breaking cracks has been studied by many authors in recent years. Reference:; to papers on scattering by surface-breaking cracks can be found in [1,2]. The corresponding problem of cavities at the surface and topographic irregularities has been studied in seismology (see, for example, [3,4]). Almost all the studies have dealt with two-dimensional problems (for references to some 3-D scattering see [5]).In this paper we have studied the general three-dimensional problem of elastic wave scattering by surface-breaking cavities of arbitrary shape using a hybrid method which combines the finite element representation of the interior field with the boundary integral representation of the exterior field. The advantage of the method is that it is suitable for analyzing scattering by arbitrarily shaped and multiple cavities. In this regard the method is similar to that used in [1], where the outside field was represented in terms of multipolar potentials. 1be details of the present method can be found in [6]. Figure 1 shows the geometry of the problem. As shown, homogeneous, isotropic, linearly elastic half-space containing a cylindrical pit of arbitrary surface shape with axis parallel to the y-axis (not shown) is considered. The two artificial boundaries B and C divide the medium into two regions. 1be interior region R 1 is bounded by the boundary B, the pit surface and part of the free surface. 1be exterior region Ro is bounded by the free surface and the contour C and extends to infinity in the x, y, and z directions. The area between the contours Band Cis shared by both regions. We consider plane harmonic P or SV-wave incident at an arbitrary angle to theY-axis (see Fig. 2). FORMULATION 63