This paper deals with the frequency band structure and band-gap analysis of the thermoelastic wave propagation in a one-dimensional (1D) porous metamaterial. The porous metamaterial is made of an infinite number of periodic unit-cells. Each unit-cell is made of two different sections, with one of them being made of an isotropic material without any voids and the other one being made of a porous material including many micro-voids. The governing equations of the considered problem are based on the Lord-Shulman theory of the generalized coupled thermoelasticity for heat conduction, considering the effects of temperature and porosity in the equation of motion, and considering the effects of temperature and displacement in the volume fraction balance equation. The frequency dispersion curves are computed using a combined analytical method based on the transfer matrix method. The effects of the micro-voids in the porous section of a unit-cell on the frequency band structures and band-gaps are investigated and discussed in details. The results show that the coupling effects between the temperature-volume fraction fields and also between the displacement-volume fraction fields influence the frequency dispersion curves of the thermoelastic wave propagation in the porous metamaterials. The proposed approach can be employed for the analysis of the thermoelastic and elastic wave propagation problems in porous metamaterials and/or metamaterials with distributed micro-voids as micro-defects. It is shown that the frequency band-gaps can be tuned by the variations in the coefficients of the volume fraction balance equation.

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