Ultrasonic guided wave (UGW) technologies are powerful nondestructive testing techniques to characterize near surface materials and evaluate integrity of materials or structures. Due the presence of boundaries, the guided waves show a strong dispersive behavior, i.e. the phase velocity and attenuations vary with frequency-content of wave package. The dispersions of guided waves depend not only to the material properties but also on the thickness of the structure under investigation. This feature allows UGW techniques to extract information on geometrical and/or material properties of structures from the measured dispersion curves. One of major issue in this problem is how to calculate efficiently the dispersion curves of all modes in the studied frequency range which will serve later to the inversion task. The Semi-Finite Element Method (SAFE) is one of most popular technique for computing the dispersion of guided waves in structures thanks to its effectiveness in studying of functionally-graded or arbitrary cross-section waveguides. However, the computational cost when using SAFE increases fast when we need to evaluate higher-modes and/or at higher frequencies. At very high frequency, using conventional high-order Lagrangian interpolation function does not allow to improve the situation because it leads to numerical issues when solving eigenproblems. 

The objective of this work is to study the effectiveness of using Non-Uniform Rational B-spline (NURBS) basis functions in the context of SAFE method for analyzing the wave propagation in waveguides. The Isogeometric Analysis (IGA) uses the NURBS basis functions as a powerful tool from the Computer Aided Design (CAD) to represent not only the complex geometries but also to construct shape function for finite element analysis. The NURBS basis functions have some advantage such as higher continuity across the element boundaries, partition of unity, linear independence and compact support. 

In this paper we first present how to implement the NURBS basis function in the SAFE formulations. Next, convergences studies are shown by considering a 2D constant-thickness anisotropic elastic plate. Three cases of material's heterogeneity over thickness were investigated: (i) homogeneous plate; (ii) functionally-graded plate; (iii) multilayer plate (with strong contrast of rigidities between layers). The results were compared with the ones obtained by analytical methods and by conventional SAFE method. For all of cases, the dispersion curves evaluated by using enriched-NURBS basis have a significant better precision than using conventional Lagrangian elements (for the same number of degrees of freedom), especially for the higher modes (e.g. A5, S5 or higher).