Comparative Study of Matrix Methods for Modeling the Dispersive Character of Ultrasonic Guided Waves

This paper presents a comparative study of various matrix methods for obtaining the dispersion curves of ultrasonic guided waves in anisotropic media for both planar and cylindrical geometries. First, the mathematical formulation of the problem is introduced. Then, matrix methods are employed to generate the characteristic dispersion functions, with a particular focus on multilayer structures. To simplify the problem and enhance convergence, the formulation of Lamb modes is separated from that of shear modes. Dispersion curves are then plotted for single and multilayer planar and cylindrical geometries of propagating modes, with each case identifying the different modes obtained and explaining their symmetry characteristics. The dispersion curves are generated using a MATLAB program and compared with two software tools: Disperse Calculator for plates and GUIGUW for cylindrical structures. A perfect match is observed. A discussion is then presented to highlight the advantages and limitations of the matrix methods, offering reliable insights into which matrix method is most suitable for each type of waveguide and enabling the plotting of convergent curves with minimal computation time. Keywords: guided waves; dispersion curves; composite; laminate; matrix method; pipeline