DETERMINATION OF THE TIME ARRIVALS OF DIV ERGENT ACOUSTICAL WAVE-FRONTS IN AN ANISOTROPIC PLATE

The present work is an attempt to extend to the acoustics of anisotrop ic media the basic principles of optics (i.e. Fermat, and Huyghens pri nciples). The acoustical case is much more intricate because of the po ssibility of existence of the cuspidal caustics. Firstly, one discusse s the mathematical transformation between phase and group wavespeeds. Then, the problem of the reflection of a divergent acoustical ray onto an interface is studied with the help of Huyghens construction. A gen eralization of the classical refraction law is obtained. Such a result can also be derived from Fermat principle. It is possible to numerica lly verify the absence of precursor on the converted mode, due to the non-existence of caustics after reflection. A discussion on the so-cal led Cagniard-de-Hoop contours is introduced, as well as a numerical pr ocedure to compute the direction of the reflected ray. Different cases , depending on the source dimension (point-like or line) and on the or ientation cut of the anisotropic solid, are discussed. The extension o f the study to several reflections is proposed. Special attention is a lso devoted to the analysis of the head wavefront reflection. Last, so me experimental results dealing with the measurements of group wavespe eds in a transversely isotropic composite material are described. The present study will be followed by the computation of the Green functio ns and the comparison with experimental displacement fields for variou s anisotropic solids.