Generalized thermoelastic band structures of Rayleigh wave in one-dimensional phononic crystals

In this paper, the band structures of TE (thermoelastic) Rayleigh wave in one-dimensional phononic crystals under steady-state thermal environment are investigated in the context of Green-Naghdi theory. The general solutions of the coupled equations are obtained firstly. Then according to the mechanical and thermal boundary conditions, the phase velocity and the transfer matrix between two adjacent units are derived by regarding the variables of the mechanical and thermal fields as a generalized state vector. The expression of band structures for real and imaginary wave vectors is fabricated on the basis of Bloch-Floquet theorem. Numerical results of the band structure of TE Rayleigh wave in Aluminum/Epoxy phononic crystal are illustrated and discussed. It is demonstrated that the band structure of TE Rayleigh wave is composed of elastic and thermal bands and that the thermoelasticity can affect the transmission ability of band gaps as well as narrow down the band gap width, which is also remarkably influenced by the filling fraction ratio. The work presented in this paper can expand the application of phononic crystals to the multi-physical field coupled with thermoelasticity.