Complex frequency band structure of periodic thermo-diffusive materials by Floquet–Bloch theory

Abstract

This work deals with the micromechanical study of periodic thermo-diffusive elastic multi-layered materials, which are of interest for the fabrication of solid oxide fuel cells. The focus is on the dynamic regime that is investigating the dispersive wave propagation within the periodic material. In this framework, a generalization of the Floquet–Bloch theory is adopted, able to determine the complex band structure of such materials. The infinite algebraic linear system, obtained by exploiting both bilateral Laplace transform and Fourier transform, is replaced by its finite counterpart, resulting from a proper truncation at a finite number of considered unknowns and equations. A regularization technique is herein useful to get rid of the Gibbs phenomenon. The solution of the problem is, finally, found in terms of complex angular frequencies, corresponding to a finite sequence of eigenvalue problems for given values of the wave vector. The paper is complemented by numerical examples taking into account thermo-mechanical coupling. The frequency band structure of the periodic thermo-diffusive elastic material is found to be strongly influenced by the interaction between thermal and mechanical phenomena.