Two and Three-Dimensional Computation of Dispersion Curves of Ultrasonic Guided Waves in Isotropic Plates by the Spectral Collocation Method

The field of non-destructive evaluations (NDE) using ultrasonic waves is widely used in industry to guarantee the safety and proper functioning of materials. Thus, mastering the dispersion curves of propagation waves in a material is an essential first step. This paper presents a numerical approach used for plotting the dispersion curves of cross-section ultrasonic guided waves. The spectral collocation method (SCM) described here can turn the set of partial differential equations for sound waves into an eigenvalue problem. In order to evaluate the efficiency of this method for an isotropic aluminum plate, we have established algorithm executed with Matlab program. The results were compared with a classical bisection zero-finding method, the stiffness matrix method, and SAFE method. The results found confirm that the SCM remains conceptually simpler and depends on the differentiation matrices used. Finally, the method proves its accuracy, its calculation speed and its capacity to compute the phase velocity and wavenumber curves as well as the complete three-dimensional dispersion spectrum which includes both propagative (real wavenumber) and non-propagative modes (complex wave number).