Wave propagation in granular dimers mounted on linear elastic foundation

The current study dwells on the wave propagation in one-dimensional periodic granular dimer (diatomic) chain mounted on linear elastic foundation. We invoke multiple time scales and partition the dynamics of the perturbed dimer chain into slow and fast components. An analytical procedure is developed for estimating primary pulse amplitude evolution resulting in a nonlinear map relating the relative displacement amplitudes of two adjacent beads. The evolution predicted by the method of maps is in good agreement with the numerical simulation of the original system. This work forms a basis for application of the devised methodology to weakly coupled granular dimers which finds practical relevance in designing shock mitigating granular layers.