Frequency limit determination for the homogenization of layered composites

A novel approach, based on spectral analysis, for determination of the upper frequency bound for the homogenization domain is developed. The method is based on displacement field analysis, which is calculated using the recursive transfer matrix. It makes up a description of the equivalent homogenous material associated to the multilayer in the low frequency area. Inside the homogenization domain the displacements field perpendicular to layers, in term of deepness, are plotted. A fast-Fourier transform (FFT) processing is used to compute the wave numbers propagating in the multilayer. The plot of the dispersion curves show that, for a limiting frequency, we may consider the multilayer as an effective homogeneous anisotropic medium supporting at the most three plane waves. Above this frequency the medium becomes dispersive and has a nonhomogeneous character. Multilayered systems resulting from the stratification of carbon-epoxy cells of the type [0/90] and [0/45/90/−45], are used for the illustrations.