Comparison of two numerical method for determination of Floquet waves in periodic multilayer

The present work deals with Floquet waves determination in multilayered composites using two methods: Floquet theory and spectral analysis of displacement field (SADF). Based on a recently-developed stiffness matrix, a recursive process gives interfacial displacement anywhere in the multilayer as function of deepness. A fast-Fourier transform (FFT) procedure has been used in order to extract the wave numbers propagating in the multilayer. The Floquet waves parameters as function of frequency and incident angle are calculated separately and a comparative study has been achieved for these two methods. For different incidence angle, the upper frequency bound of this homogenization domain is estimated. A consistent algorithm is adopted to develop an inverse procedure for the determination of the materials constants of multidirectional composite. Computational example for quasi-isotropic composite is given and compared with Floquet Homogenization method (FHM).