Abstract
We investigate the wave propagation in the two-dimensional (2D) hexagonal packing of spheres in a rectangular region using numerical simulations and theoretical analyses. The impact excitations are resolved into two distinct solitary waves with the same wave amplitude and front velocity. A universal relation between the wave front velocity and the force amplitude is obtained. One-dimensional chain models of the 2D packing are generated. The transfer of energy and momentum leads to the phenomenon of an energy equipartition in the 2D homogeneous hexagonal packed system. Moreover, the solitary wave train containing solitary waves with a decreasing amplitude is also noted. We apply conservation of energy and momentum to the collision process between spheres to predict the amplitude of the solitary wave train. Our analytical results are in good agreement with the numerical simulations.
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