Acoustic propagation in anisotropic periodically multilayered media: A method to solve numerical instabilities

Abstract

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 propagator matrix formalism. Though this formalism is very convenient, it leads to numerical instabilities for thick composites at high frequencies. 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 multilayered media. The method developed in this paper uses Floquet waves which correspond to the modes of an infinite periodically multilayered medium. They are linear combinations of the real waves propagating in each layer of the medium. The Floquet wave numbers are the eigenvalues of the propagation matrix of one period of the medium. The anisotropic periodically multilayered medium can then be considered as a dummy medium in which the Floquet waves propagate. High exponential terms can be avoided through a judicious choice of reference of the Floquet waves’ amplitudes. This method enabled us to calculate reflection coefficients up until 40 MHz, of thick composites of carbone/epoxy placed in water. Furthermore, it has permitted us to not have a limitation for a single layer of any given material, at any given frequency.