Radiation of ultrasound into an anisotropic solid

A half-space, x₃ ≤ 0, of a transversely isotropic solid whose axis of symmetry makes an angle α with the x₃-axis, is subjected to a spatially uniform time-harmonic distribution of normal surface tractions over a circular area of the plane x₃ = 0. The wave motion radiated into the half-space is investigated. Using an integral representation for the displacement components the problem is first reduced to a system of singular integral equations for the displacements on the surface x₃ = 0. This system is solved by the boundary element method over a truncated area, where use is made of recently derived simplified forms of the Green's functions. The results show the skewing of the beam as the angle between the axis of symmetry of the transversely isotropic solid and the normal to the surface of the solid is increased.