A modified model based on Guyer-Krumhansl (GK) theory is proposed for the coupled thermoelasticity in nano-sized phononic crystals (PnCs) considering energy dissipation. Frequency dispersion curves and band-gaps have been obtained for Guyer-Krumhansl thermoelastic wave propagation in PnCs using the proposed modified model. The GK-based constitutive and governing equations are derived for a nano-sized PnCs and then analytically solved to obtain the closed form solutions for temperature and displacements. The transfer matrix of each unit-cell is obtained using the thermal and mechanical continuity conditions on the interface between the two sections of each unit-cell and between two neighboring unit-cells. The frequency dispersion curves and band structures of the nano-sized PnCs are obtained using combination of the transfer matrix of each unit-cell and the Bloch–Floquet-based periodicity. Frequency band-gaps of GK thermoelastic wave propagation in a nano-sized PnCs beam have been obtained and discussed in details. Effects of some parameters such as small-scale parameter of GK theory on frequency band structures have been studied using the proposed modified GK model with energy dissipation.

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