Shock wave in a one-dimensional granular chain under Hertz contact

Scattering of shock wave by impurities in a viscoelastic granular chain

The transmission and the reflection of a shock wave by one or several impurities in viscoelastic bead chains is studied in the present paper. There is only one reflected wave for a single impurity. The amplitude of the beads oscillation increases as the initial velocity of the boundaries beads increases, while it decreases as the viscosity coefficient increases. Two reflected waves will be produced if the impurity number is larger than a critical value. This critical value depends on both the initial velocity and the viscosity coefficient. In addition, the maximum amplitude of reflected wave is a constant, when the viscosity coefficient is large enough.

Shock wave due to the short-period impact in one-dimensional plasticity bead chain

The waves in a one-dimensional (1-D) bead chain produced by a constant velocity impact in a short period are studied numerically in the present paper. It seems that in some cases, the waves look like a shock wave, while in other cases they may be composed of several solitary waves or some oscillations. These characteristics depend on both the bead parameters and the impact parameters, such as the plasticity of the bead material, the piston velocity and the impact duration. It is found that the shock structure appears if the duration of the impact is longer, while it will evolve into several solitary waves if the duration of the impact is small enough. This indicates that the bead velocity attenuates with power function. The strength of the attenuation depends on the plasticity, the piston velocity and the bead radius.