Short Pulse Dynamics in Strongly Nonlinear Dissipative Granular Chains

TL;DR

This paper investigates how pulses propagate and decay in strongly nonlinear granular chains with velocity-dependent damping, revealing two distinct dissipative wave structures with different lifetimes.

Contribution

It introduces a detailed analysis of energy decay and wave structures in dissipative nonlinear granular chains, highlighting the coexistence of solitary and shocklike waves.

Findings

Attenuating solitary waves dominate at low viscosities.

Dissipative shocklike structures have longer lifetimes.

Wave behavior depends on viscosity and initial conditions.

Abstract

We study the energy decay properties of a pulse propagating in a strongly nonlinear granular chain with damping proportional to the relative velocity of the grains. We observe a wave disturbance that at low viscosities consists of two parts exhibiting two entirely different time scales of dissipation. One part is an attenuating solitary wave, is dominated by discreteness and nonlinearity effects as in a dissipationless chain, and has the shorter lifetime. The other is a purely dissipative shocklike structure with a much longer lifetime and exists only in the presence of dissipation. The range of viscosities and initial configurations that lead to this complex wave disturbance are explored.