Almost-dispersionless pulse transport in long quasiuniform spring-mass chains: A new kind of Newton's cradle

TL;DR

This paper demonstrates a method to achieve almost dispersionless pulse transfer in long spring-mass chains by modifying boundary masses and springs, enabling efficient energy transfer with minimal loss over multiple cycles.

Contribution

It introduces a novel boundary modification technique that enables near-perfect pulse transfer in long harmonic chains, a significant advancement over traditional uniform chains.

Findings

Pulse transfer with only 1.3% amplitude loss in infinite chains.

Multiple back-and-forth pulse transfers possible before dispersion dominates.

Normal mode excitation with nearly equal frequency spacing underpins the mechanism.

Abstract

Almost-dispersionless pulse transfer between the extremal masses of a uniform harmonic spring-mass chain of arbitrary length can be induced by suitably modifying two masses and their spring's elastic constant at both extrema of the chain. It is shown that a deviation (or a pulse) imposed to the first mass gives rise to a wave packet that, after a time of the order of the chain length, almost perfectly reproduces the same deviation (pulse) at the opposite end, with an amplitude loss that is as small as 1.3 % in the infinite-length limit; such a dynamics can continue back and forth again for several times before dispersion cleared the effect. The underlying coherence mechanism is that the initial condition excites a bunch of normal modes with almost equal frequency spacing. This constitutes a possible mechanism for efficient energy transfer, e.g., in nanofabricated structures.