Abstract
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 Pade 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.
Published Version
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