Formulation of an efficient continuum mechanics-based model to study wave propagation in one-dimensional diatomic lattices

Abstract

In this paper, we formulate an efficient continuum mechanics-based model on the basis of a discrete lattice model. First, the dispersion relation of a lattice wave in a one-dimensional diatomic crystal lattice is derived. Then, the second- and fourth-order continuum models are obtained from the differential-difference equations of motion by using the Padé approximations. The results show that the proposed fourth-order continuum model can predict the dispersion behaviour of the one-dimensional diatomic crystal lattice very well in the first Brillouin zone. Furthermore, the applicability of the present model to the prediction of the dispersion behaviour of the one-dimensional diatomic lattice with internal resonator and inerter is examined. Finally, the vibration frequencies of finite diatomic lattices are calculated by both the discrete and the proposed continuum models.