Scattering of guided waves by flat-bottomed cavities with irregular shapes

This paper investigates the three-dimensional (3D) scattering of guided waves by a partly through-thickness, flat bottomed cavity with an irregular shape, in an isotropic plate. Both the scattered field and the standing field in the thinner plate beneath the cavity are decomposed on the basis of Lamb and SH waves, by including propagating and non-propagating modes. The amplitude of the modes is calculated by writing the nullity of the total stress at the boundary of the cavity, and the continuity of the stress and displacement vectors under the cavity. In the boundary conditions, the functions depend on the through-thickness coordinate, z, but contrary to the case where the cavity has a circular shape, they also depend on the angular coordinate θ. This is dealt with by projecting the z-dependent functions onto the basis of the guided wave displacements vectors, and by expanding the θ-dependent functions in Fourier series. Example results are presented for the scattering of the S0, SH0 and A0 modes by elliptical cavities of varying depth, and the scattering of the S0 mode by a cavity with an arbitrary shape. Results obtained with this model are compared with ones obtained with the finite element (FE) method, showing very good agreement.