3d Propagation of Ultrasonic Waves Through a System of Defects in an Elastic Material, with Arbitrary Reflections and Transformations

In frames of the three-dimensional problem, we study a short wavelength diffraction of elastic waves by a system of voids in the elastic medium. The defects are bounded by arbitrary smooth surfaces. The problem is reduced to a classical diffraction problem for high-frequency waves irradiated from a point source in the elastic medium by the system of voids located in this medium. We consider multiple reflections with various possible transformations of elastic waves. To study the problem, a special method is proposed, which is based on the asymptotic estimate of the diffraction integrals by the multidimensional stationary phase method. On the basis of the developed method, we obtain in explicit form the leading asymptotic term of the displacements in the diffracted field, for arbitrary cases of multiple reflections (longitudinal wave to longitudinal one and transverse wave to transverse one) and transformations (longitudinal wave to transverse one and transverse wave to longitudinal one), at the points of mirror reflections. The obtained explicit expressions for the displacements agree with the Geometrical Diffraction Theory (GDT) for elastic waves.