Plane wave propagation in 2D and 3D monodisperse periodic granular media

Plane wave propagation in periodic ordered granular media comprising of elastic spherical particles is investigated. The spheres are under zero precompression and are assumed to interact via the Hertzian contact potential. Various two- and three-dimensional granular structures such as hexagonal packing (2D and 3D), face-centered cubic and body-centered cubic packings are considered in the present study, with the plane impact either normal or oblique to the granular system. For the normal impact case, 1D chains equivalent to the 2D and 3D structures are obtained. A universal relation between the wavefront speed and the force amplitude is derived, valid for all the granular structures studied. In the angular impact case, the shear component of the amplitude of the particle velocity is found to initially decay exponentially and further in a series of linear regimes. By employing simpler models, semi-analytical predictions are obtained for the decay of shearing effect.