A coupled SAFE-BEM formulation for dispersion data extraction of leaky guided waves in waveguides of arbitrary cross-section

Abstract

The increasing applications of guided waves in the field of ultrasonic Non-destructive Evaluation (NDE) testing leads to the necessity of a mathematical tool able to extract dispersive data for waveguides of general geometrical and mechanical characteristics. Well stated analytical and numerical methods are represented, respectively, by the Matrix family methods and the Semi Analytical Finite Element (SAFE) methods. However, while the former are generally limited to simple geometries, the latter are usually not efficient in problems involving energy losses due to leakage of bulk waves. In this paper, a coupled SAFE-BEM formulation is proposed for the dispersion data extraction of leaky guided waves propagating in waveguides of arbitrary cross-section. To this end, the SAFE is used to efficiently model both the mechanical and geometrical characteristics of the waveguide, while the BEM is used to represent the external (unbounded) isotropic domain. Complex geometries with boundary corners, as well as Cauchy singular integrals typically involved in BEM formulations, are treated using a regularization procedure. The final equation for the wave propagation problem is configured as a nonlinear eigenvalue problem in which the complex wavenumbers appear implicitly. This problem is efficiently solved by means of a Contour Integral Algorithm, that does not require initial guesses of the solutions and derivative operations, providing at the same time good performances in parallelized environments. The reliability of the proposed method is demonstrated by means of a numerical application of practical interest.