A model to predict modal radiation by finite-sized sources in semi-infinite isotropic plates
Résumé
Elastic guided wave (GW) propagation is involved in various non-destructive testing (NDT) techniques of plate-like structures. The present paper aims at describing an efficient model to predict the GW field radiated by various sources attached at a distance of the straight boundary of an isotropic plate, a configuration often encountered in typical examinations. Since the interpretation of GW propagation and scattering in plates is made easier by the use of modal description, the model is derived in the classical theoretical framework of modal solutions. Direct radiation by a uniform source of finite size in an isotropic plate can be efficiently modelled by deriving Fraunhofer-like approximation. A rigorous treatment is proposed based upon i) the stationary phase method to describe the field after reflection at a plate edge, ii) on the computation of modal reflection coefficients for an arbitrary incidence relative to the edge and iii) on the Fraunhofer approximation to account for the finite size of the source. The stationary phase method allows us to easily express the amplitude of reflected modes, that is to say, the way waves spread, including reflections involving mode conversions. The computation of modal reflection coefficients for plane GW at oblique incidence was recently treated in the literature and our work for this very problem simply consisted in adapting it to the SAFE calculation we use to compute modal solutions. The overall computation of the direct and reflected contributions is numerically very efficient. Once the total field is computed at a given frequency, the time-dependent field is obtained by simple Fourier synthesis.