A stationary phase argument for the modal wave beam deviation in the time-space domain for anisotropic multilayered media

The aim of the paper is to describe the physical phenomenon of the excitation of modal waves, such as Lamb waves, in anisotropic multilayered media by a monochromatic incident beam and then by a time depending signal. A modal beam is generated in the structure and, due to the anisotropy of the media constituting the structure, is deviated with respect to the sagittal plane of the incident bounded beam. Using a stationary phase approach, it is possible to determine the deviation direction of the modal beam in the far field at a given frequency. This direction is normal to the modal curve, at the point corresponding to the main modal wave vector. Using Lagrange multipliers, it is possible to obtain the equation of an oblique plane in which the modal beam reradiates in the external fluid. As the modal waves are dispersive, the group velocity and the direction of propagation of the principal modal wave vary with the frequency. So, in the far field, for a time depending signal, the different monochromatic components of the main modal wave are found in different directions. In general, the main crest line of this modal wave packet is not a straight line.