ACOUSTIC PROPAGATION IN ANISOTROPIC PERIODICALLY MULTILAYERED MEDIA -A METHOD TO SOLVE NUMERICAL INSTABILITIES

Acoustic propagation through thick composites has become a subject of intensive study due to their application to nondestructive evaluation. The anisotropic multilayered media are now usually studied by the pro pagator matrix formalism. Though this formalism is very convenient, it leads to numerical instabilities for thick composites at high frequen cies. These numerical instabilities come from the combination of very high exponential terms which reduces the dynamics of the calculation. A very interesting case is the one of anisotropic periodically multila yered media. The method developed in this paper uses Floquet waves whi ch correspond to the modes of an infinite periodically multilayered me dium. They are linear combinations of the real waves propagating in ea ch layer of the medium. The Floquet wave numbers are the eigenvalues o f the propagation matrix of one period of the medium. The anisotropic periodically multilayered medium can then be considered as a dummy med ium in which the Floquet waves propagate. High exponential terms can b e avoided through a judicious choice of reference of the Floquet waves ' amplitudes. This method enabled us to calculate reflection coefficie nts up until 40 MHz, of thick composites of carbone/epoxy placed in wa ter. Furthermore, it has permitted us to not have a limitation for a s ingle layer of any given material, at any given frequency.