Localized energy absorbers in Hertzian chains

TL;DR

This study demonstrates that a chain of elastic spheres with embedded linear energy absorbers can efficiently convert and absorb mechanical energy from shocks, with energy absorption increasing exponentially with the number of absorbers.

Contribution

The paper introduces a mass-in-mass device within Hertzian chains and validates a numerical model to optimize energy absorption over broad frequencies.

Findings

Absorbers' energy absorption grows exponentially with their number.

The chain converts shocks into solitary waves with frequency content independent of amplitude.

A device with ten intruders can absorb most of the system's energy.

Abstract

Energy absorbers and energy-harvesting devices have been under the scope of scientists and engineers for decades to fulfill specific technological needs, mainly concerned with sound and vibration absorbers, and efficient mechanical energy converters. In this paper, as a proof of concept, we build a mass-in-mass device to study the response of a linear absorber immersed in one of the spheres composing a linear array of equal elastic spheres. Spheres barely touch one another and can thus sustain nonlinear solitary wave propagation only. The linear intruder absorbs a given amount of energy depending on the frequency content of the incident solitary wave. A numerical simulation is developed to account for the experimental finding. The validation of the numerical model allows for the theoretical study of the energy absorbed by any number of intruders, and to demonstrate that the former increases exponentially with the latter, indicating that only ten of the intruders is enough to absorb the system energy. A detailed study of the transmitted energy from an external source into the chain reveals that, due to nonlinearity, the array of spheres is able to convert almost any mechanical shock to a well defined solitary or trains of solitary waves, whose frequency content is nearly independent on the excitation amplitude. This property leads to the design of a device, which is optimized to absorb energy over a broad frequency range.