Nonlinear dynamics of two-dimensional granular periodic lattices

We study wave propagation in a damped driven discrete nonlinear two-dimensional (2D) periodic structure. The considered system is composed of identical spherical particles and subjected to harmonic horizontal base excitation, where its collective nonlinear dynamics is caused by the Hertzian contact law and the applied compressive load. The coupled equations governing the nonlinear vibrations of the considered system have been solved using an analytical-numerical solving procedure, which allows a detailed study of complex model interactions of the periodic structure. The multiple scales method coupled with standing wave decomposition were used to transform this nonlinear system into a set of complex differential equations, which has been numerically solved. Numerical simulations have been performed in order to analyze the stability, the modal interactions and the bifurcation topologies resulting from the collective dynamics of particles in contact, in a 2D configuration.