European Journal of Mechanics A/Solids 22 (2003) 283–294 Pulse propagation in plate elements E. Moreno a , P. Acevedo b,∗ , M. Castillo a a Ultrasonic Center, ICIMAF, CITMA, Calle 15 No. 551, Vedado, La Habana, 10 400, Cuba b DISCA-IIMAS-UNAM, Apdo. Postal 20-726 Admon. No. 20, 01000, Mexico D.F., Mexico Received 11 March 2002; accepted 10 January 2003 Abstract This paper describes a theoretical and experimental study of pulse propagation in plates. Specifically, this approach uses the Fourier–Laplace Transform (FLT), for the solution of the Lame equation with the boundary condition given by the transducer over one side of the plate. It is shown that a pulse in plates is formed by three fundamental components with its own dispertion relationship. Experiments were performed in elastic plates to validate the model.  2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Lamb waves; Pulses in plates 1. Introduction Dispersion in wave propagation means a relationship between the phase and group velocity with the frequency. Two mechanisms can be identified, the geometric and the viscoelastic. In the first case the geometric condition given by the vicinity of boundaries has the effect of guiding the waves producing this phenomena. In the second case the rheology of the material has a similar property on the wave propagation. Examples of geometric dispersion may be found in bars and plates. In this second case, when the plate is isotropic and has a free boundary, the harmonic solution for the transverse propagation is given by Lamb waves (Achenbach, 1973; Auld, 1990). The dispersion law obtained from Lamb waves, cannot describe the pulse propagation case neither by an harmonic superposition of Fourier components traveling with phase velocity nor by wavelets components traveling with the group velocity (Kolsky, 1964). Fig. 1 shows the dispersion curves for Lamb waves. According to this, the head of a pulse in a plate will be composed by low frequency components instead of high frequency components experimentally obtained. This situation is very similar to the one found in an isotropic rod (Tu et al., 1955) where there is the same contradiction with high frequency components at the head of the pulse experimentally obtained (Moreno, 1994). Historically, pulse propagation in isotropic plates has been analyzed using the Fourier–Laplace Transform (FLT). This tool has been applied to the transient waves generated by the application of a normal line load as a boundary condition (Achenbach, 1973). Nevertheless, the classic method can not completely describe the head part of a pulse. This paper develops a theoretical method for pulse propagation in plates with the use of the FLT. As in previous models the final solution is obtained using the inverse FLT which is evaluated in the complex plane, by the sum of the residues of the poles of the integrand. However, in this case the pole analysis is made using the zero analysis, obtaining a solution formed by three components, Lamb, cuasilongitudinal, and cuasitransversal. These all three components have their own dispersion law. Experiments of pulse propagation in plate elements are presented in order to validate the model. * Corresponding author. E-mail addresses: moreno@cidet.icmf.inf.cu (E. Moreno), pedro@uxdea4.iimas.unam.mx (P. Acevedo). 0997-7538/03/$ – see front matter  2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. doi:10.1016/S0997-7538(03)00014-7