Analysis of temperature-dependent wave propagation for programmable lattices

This study focuses on temperature-dependent wave propagation in hexagonal and square lattices, which has potential application in the design of programmable lattices. To obtain the thermal effect on the wave behaviors of the lattices, temperature fields are applied to the structures and the thermal responses of the structures are analyzed. Furthermore, the temperature-dependent wave propagation behaviors are investigated in terms of the distributions of band gaps, and phase and group velocities, based on Bloch's theorem and the principle of the finite element method. In particular, directional wave propagation and energy flow are carefully investigated. We find that increasing temperature generates negative axial forces along the elements and decreases the branches of frequencies in the band structures. The phase and group velocities show the maxima amplitude of wave propagation in the 0°, 180°, ± 60° and ± 120° directions of the hexagonal lattice. The cooling process makes the energy flow focus in these directions, while the heating process allows the energy flow of the wave propagation focus in these directions at first and then makes it dispersed. The results can be used to tune wave propagation utilizing temperature-dependent wave behavior in the lattices.