Attenuation of short strongly nonlinear stress pulses in dissipative granular chains

Attenuation of short, strongly nonlinear stress pulses in chains of spheres and cylinders was investigated experimentally and numerically for two ratios of their masses keeping their contacts identical. The chain with mass ratio 0.98 supports solitary waves and another one (with mass ratio 0.55) supports nonstationary pulses, which preserve their identity only on relatively short distances, but attenuate on longer distances because of radiation of small amplitude tails generated by oscillating small mass particles. Pulse attenuation in experiments in the chain with mass ratio 0.55 was faster at the same number of the particles from the entrance than in the chain with mass ratio 0.98. It is in quantitative agreement with results of numerical calculations with effective damping coefficient 6 kg/s. This level of damping was critical for eliminating the gap openings between particles in the system with mass ratio 0.55 present at lower or no damping. With increase of dissipation numerical results show that the chain with mass ratio 0.98 provides faster attenuation than the chain with mass ratio 0.55 due to the fact that the former system supports the narrower pulse with the larger difference between velocities of neighboring particles. The investigated chains demonstrated similar behavior at large damping coefficient 100 kg/s.