A boundary element formulation for the computation of damped guided waves

Abstract

The use of ultrasonic guided waves (GW) has increased considerably in the fields of non-destructive testing and structural health monitoring due to their ability to perform long range inspections, to probe hidden areas as well as to provide a complete monitoring of the entire waveguide. Guided waves can be fully exploited only once their dispersive properties are known for the given waveguide. To this end, in this paper a 2.5D boundary element technique is presented to extract the dispersion curves for waveguides in which material attenuation is included. Compared with other well-accepted techniques such as the Transfer Matrix Method (TMM), the Global Matrix Method (GMM) and the Semi Analytical Finite Element (SAFE) method, the proposed method is able to analyze waveguides of arbitrary cross-section by discretizing its contour only with monodimensional elements. The method is based on a regularized boundary integral formulation which leads to a nonlinear eigenvalue problem in the complex axial wavenumber for any fixed frequency. To extract the dispersion relations, the eigenvalue problem is solved in the complex wavenumber domain by using a contour integration method. The method is demonstrated through a numerical example and the results are compared with those obtained using the SAFE method.