Rainbow reflection and trapping for energy harvesting

TL;DR

This paper clarifies the distinction between rainbow reflection and trapping mechanisms in wave control, demonstrating their implications for energy harvesting using elastic metasurfaces and graded line arrays.

Contribution

It introduces a methodology to differentiate rainbow reflection from trapping, with applications to elastic wave energy harvesting on Kirchhoff-Love plates and metasurfaces.

Findings

Rainbow reflection and trapping are distinct phenomena with different energy focusing capabilities.

The methodology predicts energy trapping and conversion efficiency in elastic wave systems.

Simulations show effective energy harvesting using graded line arrays of resonant rods.

Abstract

Important distinctions are made between two related wave control mechanisms that act to spatially separate frequency components; these so-called rainbow mechanisms either slow or reverse guided waves propagating along a graded line array. We demonstrate an important nuance distinguishing rainbow reflection from genuine rainbow trapping and show the implications of this distinction for energy harvesting designs. The difference between these related mechanisms is highlighted using a design methodology, applied to flexural waves on mass loaded thin Kirchhoff-Love elastic plates, and emphasised through simulations for energy harvesting in the setting of elasticity, by elastic metasurfaces of graded line arrays of resonant rods atop a beam. The delineation of these two effects, reflection and trapping, allows us to characterise the behaviour of forced line array systems and predict their capabilities for trapping, conversion and focusing of energy.