COMBINING PHASE VELOCITY METHOD AND FEM FOR COMPUTING DISPERSION CURVES IN CURVED PLATE GUIDEWAVES

Abstract

Lamb waves are extensively used in non-destructive tests (NDT) to detect corrosion and another defects in thin plates. Several NDT methods require to compute the phase velocity of the Lamb wave, which depends on the frequency. In this work we show the potential of the combination of the phase velocity method (PVM) with the finite element method (FEM) for computing the phase velocity dispersion curve of an ultrasonic pulse traveling in a transversally annular isotropic thin plate. The FEM-PVM is based on the numerical solution of the wave propagation equations for several selected frequencies. To solve these equations, a second order difference scheme is used to discretize the temporal variable, while spatial variables are discretized with FEM. The open software FreeFem++ is used with quadratic triangular elements to compute the displacements. The phase velocity for a given frequency is obtained from the computed displacements at few points on the top of the plate. Repeating the procedure for several frequencies we compute a sample of points that are fitted to obtain an approximation of the phase velocity dispersion curve. A deeper understanding on the behavior of the phase velocity dispersion curve with respect to the plate curvature is obtained as result of an extensive experimentation with annular isotropic plates of two materials.