Continualization Method for Periodic Cauchy Materials in non-standard Thermoelasticity
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In this work, the authors propose a continualization method to investigate the Bloch waves that propagate in non-standard thermoelastic periodic materials in the framework of the Green-Lindsay theory . Focusing on the case of thermoelastic layered periodic materials, the governing field equations of the Lagrangian model are manipulated to identify equivalent multi-field gradient-type (higher order) non-local continua by establishing an equivalence between the Z-transform of the vector containing nodal fields and the spatial Fourier transform with a complex argument (or two-sided Laplace transform) of the corresponding continuum fields and, then, rewriting the kernel both as a truncated Taylor series and a Padé approximant. To verify the accuracy of the proposed method, a comparison between the homogenized Bloch spectra and the heterogeneous ones provided by performing the transfer matrix method is carried out and a remarkable agreement is observed for high frequency ranges.
