Scattering of obliquely incident guided waves by a stiffener bonded to a plate

Nondestructive testing of aerospace structures often requires their immobilization or disassembly. Structural health monitoring (SHM) can overcome these problems; the use of guided elastic waves (GW) in SHM is of great interest, because they propagate long distance in the structure thickness. Structures being stiffened, optimally positioning sensors implies to determine the number of stiffeners a wave can go through while remaining detectable. Here, the diffraction of GW by a stiffener bonded to a plate is considered. Elastic and geometric invariances along stiffener axis lead to 2D computations involving the three components of wave particle displacement, whatever its incidence on stiffener. A hybrid model is developed combining the semi-analytical finite element method for GW propagation and a finite element method (FE) for the stiffener diffraction. Optimal hybridization is obtained thanks to the development of transparent boundaries of the FE domain Such boundaries have been obtained for GW normally incident onto a scattering feature, thanks to Fraser's bi-orthogonality relation, which unfortunately does not hold for oblique incidence. A numerical approach is developed to numerically approximate it, then, to derive boundary conditions in the wanted form. Their use minimizes the size of the FE domain and avoids any artificial reflection. They provide a mean for projecting diffracted fields on modes reflected on or transmitted through the stiffener; corresponding coefficients are obtained as functions of the direction of incidence.