Diffraction of flexural waves by finite straight cracks in an elastic sheet over water

The diffraction of long-crested incident waves propagating within a thin flexible elastic sheet floating on water by narrow cracks is considered. The cracks are straight and each of finite length and must be parallel to one another. This arrangement lends itself to the use of Fourier transform methods, which allows the solution to a simpler problem to be used. For N cracks, 2N coupled integral equations results for 2N unknown functions related to the jump in displacement and slope across each crack as a function of distance along the cracks. These integral equations are hypersingular but, in approximating their solution using Galerkin's method, a judicious choice of trial function provides maximum simplification in the algebraic equations which result. Numerical results focus on the diffracted wave amplitudes, the maximum displacement of the elastic sheet and the stress intensity factor at the ends of the cracks. For two side-by-side cracks, large resonant motion can occur in the strip between the cracks.