Study of Lamb waves based upon the frequency and angular derivatives of the phase of the reflection coefficient

Abstract

This article deals with the introduction of a new method which allows the complete characterization of an elastic plate, on the one hand, in terms of resonances and, on the other hand, in terms of Lamb wave propagation. It is based upon the study of the derivatives of the reflection coefficient phase, considered either as a function of a frequency variable or as a function of an angular variable. When the Breit–Wigner approximation is valid, i.e., when the poles of the reflection coefficient are close to the real axis, the comparison with the resonant scattering theory (RST) leads to the characterization of frequency or angular resonances in terms of positions and widths, by means of the location and of the magnitude of the phase derivative peaks. Moreover, this method allows one to establish the important link between this resonant theory derived from the RST and the normal mode theory of propagation. So, the width of a resonance is explicitly related to the imaginary part of the wave vector of the associated Lamb wave.