Harmonic wave propagation in materials with periodic beam-structure

Abstract

The characteristics of harmonic waves propagating in periodic beam structures are investigated. For this purpose, a very effective method for the calculation of dispersion relations of elastic waves in these materials is developed by applying dynamic theory of crystal lattices to discrete models of periodic beam structures. This method is applicable to general three-dimensional periodic beam structures. Results presented show that the solutions converge to the exact solution as the number of atoms in the discrete models increases. The dispersion relations of plane harmonic waves in the micropolar continuum model, developed in a previous study, are also calculated. They are compared with the exact solutions to examine the applicability of the continuum models to dynamic problems.