In this paper, a meshless collocation method based on the generalized finite difference (GFD) method is employed for the band structure analysis of thermoelastic waves propagating in the cylindrical phononic crystal (PC). The Green-Naghdi (GN) theory of the generalized coupled thermoelasticity with energy dissipation and the Bloch\\\'s theorem are adopted to compute the dispersion relation of thermoelastic waves. The proposed GFD-based meshless collocation method is used to predict the frequency range of the band-gaps and to analyze the effects of the material parameters and the thickness of each layer (sub-cylinder) in a unit-cell on the band-gap property of thermoelastic waves propagating in the cylindrical PCs. The effects of the variations in the layer thicknesses in each unit-cell on the thermoelastic wave band structures are studied in detail. Also, the influences of the key material parameters on the frequency band structures of the thermoelastic waves are investigated. It will be shown that the dimensionless speed of the thermal wave influences the band-gaps more remarkably than other dimensionless parameters such as the dimensionless speeds of the purely elastic dilatational and shear waves, the damping coefficient and the thermoelastic coupling parameter.

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