Power-law Behavior Of Confined Energy And Solitary Wave Propagation In Granular Media

Granular material research has received more and more attention in recent years,because the particulate matter is prevalent in people's daily lives and applied to all aspects of production and life.There have many potential value,such as the creation of shock-absorbing materials,acoustic lenses,switches,logic elements,and energy-harvesting system,etc.In the paper,we in order to design a better grain protection device,studied the energy dissipation of composite particle chain system in detail.In addition,a special interaction solitary wave generated in 2D particle system was found,and analyzed the propagation characteristics.First of all,we according to the “particle container” protection device design ideas,re-simulated the impact energy dissipation process in 1D composite particle chain.It's verified that the power-law behavior of confined energy in 1D composite particle chain container satisfies the power exponent relationship:E_R At^-?,and there is a crossover in the energy dissipation process.On both sides of the crossover,two different dissipation exponent ? are presented.This is because the “gap” between the particle of the heavy district is opened.In other word,that is the transition from the compressed state to the discreted state process leads to different energy dissipation laws.Through our further study,there should also be a crossoverbt,when follow the another energy dissipation exponent.We demonstrated that the reason for this is due to the change in structural state in the light district,so the “gap” between the particle of the light district is opened.Finally,we further study the specific relationship between the energy decay exponent and the mass ratio of light and heavy particles and the Hertz exponent.Then we investigate the wave propagation in a two-dimensional?2D?hexagonal packing restricted within rectangular region in which boundary spheres arranged in the shape of zig-zag are subjected to the planar impact,using numerical simulation and theoretical analyses.We observe that the impact excitations are resolved into two distinct solitary waves with the same amplitude and wave front velocity respectively propagating down the two columns.One-dimensional chain equivalent to the 2D packing and a universal relation between the wave front velocity and the force amplitude are respectively derived.The phenomenon of momentum transfer and energy equipartition are observed in the 2D homogeneous hexagonal packing.Moreover,the solitary wave train with amplitude decreasing is observed.We applyconservation of energy and momentum to collision process between spheres to predict the amplitudes of the solitary wave train.Our analytical results are in good agreement with the numerical simulations.