  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 (SOFCs). 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 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 overall behaviour
is found to be strongly influenced by the interaction between thermal and
mechanical phenomena.
