Design of a thermoelastic metafilter through non-local continualization methods

This paper is dedicated to the conceptual design of periodically microstructured metafilters/waveguides, made of thermoelastic material, described by a generalized thermoelastic theory with two relaxation times. In the general case of a three-dimensional material, the governing equations are first transformed into the s-space and the wave propagation is analysed through the multidimensional Floquet–Bloch transform. Special focus is then given to the case of a layered material. By exploiting the transfer matrix method, the spectral properties are analysed, focusing on the propagation of Bloch waves and the interaction between mechanical and thermal variables. Furthermore, two novel non-local continualization methods are proposed, addressing high-frequency approximations across different wave regimes and identifying non-local continua in general thermoelasticity contexts. The paper introduces innovative methods for spectral characterization, including a representation in the space of invariants and comparisons between continualization and homogenization techniques. Additionally, a novel method based on Padé approximants accelerates spectrum convergence.