Wave propagation in an elastic lattice with non-reciprocal stiffness and engineered damping

TL;DR

This paper explores how combining nonreciprocal stiffness with engineered damping in an elastic lattice enables independent control of wave amplification, velocity, and frequency, advancing active metamaterial design.

Contribution

It introduces a decoupled control mechanism using nonreciprocal stiffness and gyroscopic damping, allowing independent tuning of wave properties in elastic lattices.

Findings

Nonreciprocal stiffness controls wave amplification rate.

Gyroscopic damping independently tunes wave velocity and frequency.

Enhanced net amplification for slower waves and boundary wave interference phenomena.

Abstract

Nonreciprocal wave propagation allows for directional energy transport. In this work, we systematically investigate wave dynamics in an elastic lattice that combines nonreciprocal stiffness with viscous damping. After establishing how conventional damping counteracts the system's gain, we introduce a non-dissipative form of nonreciprocal damping in the form of gyroscopic damping. We find that the coexistence of nonreciprocal stiffness and nonreciprocal damping results in a decoupled control mechanism. The nonreciprocal stiffness is shown to govern the temporal amplification rate, while the nonreciprocal damper independently tunes the wave's group velocity and oscillation frequency. This decoupling gives rise to phenomena such as the enhancement of net amplification for slower-propagating waves, and also boundary-induced wave interference arising from divergent and convergent reflected wave trajectories with varying growth rates. These findings provide a theoretical framework for designing active metamaterials with more versatile control over their wave propagation characteristics.