Pulse propagation in a chain of o-rings with and without precompression

TL;DR

This paper develops an analytic binary collision approximation to study pulse propagation in chains of o-rings, comparing predictions with numerical simulations across various precompression conditions.

Contribution

It extends the binary collision approximation to precompressed chains, enabling analytical pulse velocity calculations in more general settings.

Findings

Analytic pulse velocity results match numerical simulations.

The method applies to chains with different precompression types.

Provides a generalized theory for pulse propagation in precompressed granular chains.

Abstract

We implement a binary collision approximation to study pulse propagation in a chain of o-rings. In particular, we arrive at analytic results from which the pulse velocity is obtained by simple quadrature. The predicted pulse velocity is compared to the velocity obtained from the far more resource-intensive numerical integration of the equations of motion. We study chains without precompression, chains precompressed by a constant force at the chain ends (constant precompression), and chains precompressed by gravity (variable precompression). The application of the binary collision approximation to precompressed chains provides an important generalization of a successful theory that had up to this point only been implemented to chains without precompression, that is, to chains in a sonic vacuum.