The elastodynamic model of wave-telegraph type for quasicrystals

In this work we propose the elastodynamic model of wave-telegraph type for the description of dynamics of quasicrystals. Phonons are represented by waves, and phasons by waves damped in time and propagating with finite velocity. Therefore, the equations of motion for the phonon fields are of wave type and for the phason fields are of telegraph type. The proposed model constitutes a unified theory in the sense that already established models in the literature can be recovered as asymptotic cases of it. The equations of motion for the displacement fields in the theory of incompatible and compatible elastodynamics of wave-telegraph type of quasicrystals are derived.