Ultrasonic wave propagation in an anisotropic cladding with a wavy interface

The propagation of ultrasonic waves in a thick plate with a cladding is investigated in the two-dimensional case. The surfaces of the plate are traction-free except where an ultrasonic probe is attached and emits waves into the plate. The plate is made of two different materials, the base material and the cladding, and these are both allowed to be anisotropic. The interface between the base material and the cladding is assumed to be wavy (sinusoidal) and this is common in practice for welded claddings. The null field approach is used to solve the wave propagation problem. Thus the starting point is the (surface) integral representations in the two materials. The Green's tensors are chosen as the half space Green's tensors as only the integrals along the interface then remain. The Green's functions are expanded in Fourier transforms along the interface and the surface fields are likewise expanded. Applying the periodicity of the interface a discretized set of equations remains. For the sinusoidal interface all integrals can be computed analytically which leads to an efficient numerical scheme. Some numerical results show the influence of the anisotropy and the wavy interface.