Lattices With Internal Resonator Defects

TL;DR

This paper investigates chains with internal resonator defects, exploring their energy transmission, reflection, and trapping capabilities through experiments, simulations, and theory, focusing on linear and nonlinear defect effects and energy confinement.

Contribution

It introduces a comprehensive analysis of defect-induced energy dynamics in chains with internal resonators, including multi-defect interactions and energy confinement mechanisms.

Findings

Defects can effectively trap and confine energy in chains.

Nonlinear defects exhibit different energy transmission properties than linear ones.

Experimental results align well with numerical simulations and theoretical predictions.

Abstract

We consider a variety of settings involving chains with one or more defects stemming from the introduction of nodes bearing internal resonators. Motivated by experimental results in woodpile elastic lattices with one or two defects, we consider a variety of different theoretical scenarios. These include multi-defect chains and their ability to transmit, reflect, and especially trap energy; they also include settings with linear vs. nonlinear defects of variable interaction exponent. Moreover, they involve defects which are spatially separated and either statically, or more effectively dynamically, enable the confinement of energy between the separated defects. Wherever possible, comparisons of the experiments with numerical simulations, as well as with theoretical intuition are also offered, to provide a justification for the observed findings.