Observation of two-wave structure in strongly nonlinear dissipative granular chains

TL;DR

This study observes a two-wave structure in strongly nonlinear dissipative granular chains, revealing the dynamics of primary solitary-like pulses and secondary shock-like pulses influenced by viscosity and nonlinearity.

Contribution

It demonstrates the existence and evolution of a two-wave structure in dissipative granular chains under impact, highlighting the transition from solitary to shock-like waves due to viscosity effects.

Findings

Primary pulse resembles a solitary wave in a sonic vacuum.

Secondary pulse is shock-like and persists longer due to viscosity.

At high viscosity, the two pulses merge into a single dissipative shock.

Abstract

In a strongly nonlinear viscous granular chain under conditions of loading that exclude stationary waves (e.g., impact by a single grain) we observe a pulse that consists of two interconnected but distinct parts. One is a leading narrow "primary pulse" with properties similar to a solitary wave in a "sonic vacuum." It arises from strong nonlinearity and discreteness in the absence of dissipation, but now decays due to viscosity. The other is a broad, much more persistent shock-like "secondary pulse" trailing the primary pulse and caused by viscous dissipation. The medium behind the primary pulse is transformed from a "sonic vacuum" to a medium with finite sound speed. When the rapidly decaying primary pulse dies, the secondary pulse continues to propagate in the "sonic vacuum," with an oscillatory front if the viscosity is relatively small, until its eventual (but very slow) disintegration. Beyond a critical viscosity there is no separation of the two pulses, and the dissipation and nonlinearity dominate the shock-like attenuating pulse which now exhibits a nonoscillatory front.