On the wave dispersion and non-reciprocal power flow in space-time traveling acoustic metamaterials

TL;DR

This paper analytically explores non-reciprocal wave dispersion in space-time modulated acoustic metamaterials, revealing unique propagation features and enabling the design of sub-wavelength one-way wave guides.

Contribution

It introduces a mathematical framework for analyzing non-reciprocal dispersion and power flow in space-time modulated acoustic metamaterials, highlighting novel wave control capabilities.

Findings

Dispersion relations show break-up of propagation modes and one-way band gaps.

Validation of theoretical results with transient displacement responses.

Potential for designing sub-wavelength low-frequency one-way wave guides.

Abstract

This note analytically investigates non-reciprocal wave dispersion in locally resonant acoustic metamaterials. Dispersion relations associated with space-time varying modulations of inertial and stiffness parameters of the base material and the resonant components are derived. It is shown that the resultant dispersion bias onsets intriguing features culminating in a break-up of both acoustic and optic propagation modes and one-way local resonance band gaps. The derived band structures are validated using the full transient displacement response of a finite metamaterial. A mathematical framework is presented to characterize power flow in the modulated acoustic metamaterials to quantify energy transmission patterns associated with the non-reciprocal response. Since local resonance band gaps are size-independent and frequency tunable, the outcome enables the synthesis of a new class of sub-wavelength low-frequency one-way wave guides.