The Phase Gradient Method: Application to the Obtaining of the Dispersion Curves and the Energy Velocity of Anisotropic Plate Modes

In a previous paper [1], it was shown that the phase gradient method, i.e., the study of the derivatives of the phase of the reflection coefficient with respect to the frequency and the incidence angle enables to obtain frequency and (polar) angle quality factors for the guided modes of anisotropic plates as well as for isotropic plates. For isotropic plates, these quality factors lead to the obtaining of the dispersion curves of the guided modes and of their energy velocity whose direction is in the incidence plane. For anisotropic plates, the component of the energy velocity parallel to the incidence plane is still provided by the frequency and polar angle quality factors. The normal component may be obtained by taking into account a third quality factor. It is an azimuthal angle quality factor derived from the phase derivative with respect to the deviation angle between the incidence plane and a symmetry plane of the anisotropic material. Results for a plate of cubic symmetry are exhibited. They are compared to those obtained from energy calculations that involve the kinetic and strain energies as well as the Poynting vector.