Scattering of Lamb waves by a circular cylinder

Following our previous attempt at the scattering from a cylinder in a slab to the incidence of a guided shear wave, we hereby discuss the scattering by an elastic cylinder embedded in an isotropic plate for a variety of bonding states to incidence of the fundamental Lamb wave modes S0 and A0 at the low-frequency regime. The plate is divided up into three regions by introducing two imaginary planes located symmetrically some distance from the cylinder and perpendicular to surfaces of the plate. The wave fields in various regions are expanded either into cylinder wave modes or into Lamb wave modes. A system of equations determining the coefficients of expansion is obtained according to the traction-free boundary conditions on the plate walls and the displacement and stress continuity conditions across the virtual planes. By taking an appropriate finite number of terms of the infinite expansion series and some selected points on the two properly chosen imaginary planes and the surfaces of the plate through convergence and precision tests, a matrix equation to numerically evaluate the expansion coefficients is found. Coefficients of the reflection and transmission versus the normalized radius of the cylinder in welded, slip, and cracked interfacial conditions are numerically computed. In the low-frequency range, the relative errors are found to be less than 1%. Contrast curves of the reflection coefficient for the cylinder of nearly all permissible size in perfect and imperfect interfacial bonding are shown and prominent differences are noted.