Pulse propagation in decorated granular chains: An analytical approach

TL;DR

This paper presents an analytical method to understand pulse propagation in decorated granular chains by simplifying the system into undecorated chains with effective parameters, enabling straightforward calculation of propagation properties.

Contribution

It introduces a novel analytical approach that replaces decorated chains with effective undecorated chains, extending previous binary collision approximations.

Findings

Derived simple analytic expressions for pulse propagation

Validated the approach with numerical comparisons

Provided insights into the effect of small granules on pulse dynamics

Abstract

We study pulse propagation in one-dimensional chains of spherical granules decorated with small grains placed between large granules. The effect of the small granules can be captured by replacing the decorated chains by undecorated chains of large granules of appropriately renormalized mass and effective interaction between the large granules. This allows us to obtain simple analytic expressions for the pulse propagation properties using a generalization of the binary collision approximation introduced in our earlier work [Phys. Rev. E in print (2009); Phys. Rev. E {\bf 69}, 037601 (2004)]