Attenuation of short strongly nonlinear stress pulses in dissipative granular chains

TL;DR

This study investigates how strongly nonlinear stress pulses attenuate in dissipative granular chains, revealing that chain composition and damping levels significantly influence pulse decay and wave structure.

Contribution

The paper provides experimental and numerical analysis of pulse attenuation in granular chains with different mass ratios, highlighting the role of damping in wave behavior and energy dissipation.

Findings

Faster attenuation in the chain with mass ratio 0.55 at lower damping.

Numerical results agree with experiments using an effective damping coefficient of 6 kg/s.

Different wave structures observed at zero and intermediate damping, similar at high damping.

Abstract

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. However with increase of dissipation numerical results show that the chain with mass ratio 0.98 provides faster attenuation than 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 different wave structure at zero dissipation and at intermediate damping coefficients and the similar behavior at large damping.