Lamb wave scattering from a circular partly through-thickness hole in a plate

Abstract

The scattering problem of an incident plane S 0 Lamb wave in a plate with a circular partly through-thickness hole is considered in this paper. A 3D approach is used where the wave fields in the outer part outside the hole and in the inner part beneath the hole are expanded in the possible Lamb modes and the horizontally polarized shear modes. Both propagating modes and evanescent modes are included in the expansions. The expansion coefficients are obtained by utilizing the boundary conditions at the hole boundary and the continuity conditions below the hole. A linear system of equations for the expansion coefficients is obtained by projecting the different boundary conditions onto an orthogonal set of projection functions. A second approach is also presented, mainly for validation of the 3D model. This approach is based on the lowest order plate theories for extensional and flexural motion. Consequently, this model is only valid for very low frequencies. The two plate theories are combined and the wave fields in the different regions of the plate are obtained from the boundary conditions at the hole. Comparisons are made between the two different models for low frequencies and they show good agreement. A few examples are also given from the 3D model for higher frequencies where the plate theory model is not valid.