Comparative Study of the Spectral Method, DISPERSE and Other ‎Classical Methods for Plotting the Dispersion Curves in ‎Anisotropic Plates

This paper presents a comparative study of different methods for obtaining the dispersion curves of ultrasonic guided waves in anisotropic media. First, we present the classical algorithms used to find zeros and propose some improvements. Next, the spectral method is explained for modeling the guided waves in anisotropic materials while presenting a technique that can distinguish the modes present in the structure. The dispersion curves are plotted using a Matlab program and the results are compared with those of the DISPERSE software. In addition, a comparison with the results obtained by Nayfeh’s works in the field of Nondestructive testing by ultrasonic guided waves is included. Then a discussion is developed to highlight the strengths of the spectral method. For proper non-destructive testing, we need reliable information about the modes that propagate in our waveguide. Both analytical and spectral approaches have limitations in obtaining the exact displacement and stress profiles in a plate media. To remedy this, normalization by the acoustic power is essential. Next, the displacement and stress fields obtained from the spectral method of the modes that can propagate in the plate are compared to those obtained analytically. A very good concordance is then noticed. Based on the results obtained, the spectral method presents a very good alternative for obtaining dispersion curves. It is a convergent method, stable, easy to implement with a very low calculation time.