Analysis of ideal models of real nonlocal acoustic and elastic metamaterials

Abstract

Nonlocal coupling in acoustic and elastic systems has received growing attention for its potential to expand the capabilities of active metamaterials. Previously, we have shown experimentally how nonlocality imposed through action at a distance, where signals from disturbances at one location are used to drive actuators at separate locations, gives rise to unique scattering characteristics, namely highly nonreciprocal transmission. We showed how the mathematical models for these experimental systems were excellent predictors for real system behavior, and as such, represented powerful experimental design tools. However, these models were elaborate, incorporating the characteristics of real sensors and actuators, electronic controllers, and material properties and geometries, consequently obscuring the underlying nonlocal physics responsible for their unique behavior. Here, we present simplified models of these real systems that feature closed form expressions for system scattering characteristics, allowing for the identification of relevant dimensionless quantities and revealing how the interactions of those quantities affect both system performance and stability. We compare and contrast ideal models for both acoustic and elastodynamic nonlocal systems, highlighting how each ideal model is qualitatively representative of its real counterpart, thus providing a pathway to a deeper understanding and further exploration of nonlocality in wave-bearing systems.