Lattices with internal resonator defects

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.

A simple model of radiating solitary waves

“…See Figure 1 for a representative depiction. A similar phenomena occurs in simulations of mass-in-mass lattices [16,9], as well as in a variety of models for the evolution of capillary-gravity waves [4,5,33], though in this latter case the emission runs ahead of the solitary wave. Simulations of water waves over variable bottom topography evoke a similar dynamic [13,25,22,26].…”