Manipulating waves by distilling frequencies: a tunable shunt-enabled rainbow trap

TL;DR

This paper introduces a tunable broadband wave attenuation method using shunted piezoelectric inclusions, creating a rainbow trap that distills multiple frequencies from wavepackets without requiring periodic structures.

Contribution

It demonstrates a novel approach to broadband wave attenuation by tuning circuits to resonate at different frequencies, enabling spectral manipulation without strict periodicity.

Findings

Successfully distills seven frequencies from wavepackets

Creates a tunable rainbow trap for broadband wave attenuation

Provides detailed guidance for designing shunted piezoelectric experiments

Abstract

In this work, we propose and test a strategy for tunable, broadband wave attenuation in electromechanical waveguides with shunted piezoelectric inclusions. Our strategy is built upon the vast pre-existing literature on vibration attenuation and bandgap generation in structures featuring periodic arrays of piezo patches, but distinguishes itself for several key features. First, we demystify the idea that periodicity is a requirement for wave attenuation and bandgap formation. We further embrace the idea of "organized disorder" by tuning the circuits as to resonate at distinct neighboring frequencies. In doing so, we create a tunable "rainbow trap" [Tsakmakidis et al. Nature 450, 397-401 (2007)] capable of attenuating waves with broadband characteristics, by "distilling" (sequentially) seven frequencies from a traveling wavepacket. Finally, we devote considerable attention to the implications in terms of packet distortion of the spectral manipulation introduced by shunting. This work is also meant to serve as a didactic tool for those approaching the field of shunted piezoelectrics, and attempts to provide a different perspective, with abundant details, on how to successfully design an experimental setup involving resistive-inductive shunts.