Crossover in the power-law behavior of confined energy in a composite granular chain

We present a numerical study of the impact energy decay in a composite granular chain containing two heavy and one light sections. We observe a marked crossover in the power-law behavior of the impact-energy decay. The average reflection frequency first increases with a decreasing acceleration, and arrives at its maximum at "crossing" time then decays almost exponentially. The analysis demonstrates that this phenomenon is related to the structural transition from compression to dilation state in both heavy-particle sections. The further calculations suggest the dependence relation of the power-law exponent (gammacb) in compression state on the mass ratio (m2/m1) and the Hertz law exponent (n) of the composite granular chain gammacb approximately (m2/m1)1/(n+1).