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

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.

Non-reciprocal wave phenomena in energy self-reliant gyric metamaterials

“…Note that band gaps corresponding to left-propagating waves up-shift a/o down-shift by an amount Ω p ; a behavior which is in agreement with the observed robustness 33 and quantization 50 of non-reciprocal band gaps in space-time modulated systems. As indicated earlier, the GMM uniquely maintains stability at fast modulation speeds, in contrast to stiffness modulation in elastic metamaterials 29 . An example of a fast modulation is Ω p = 1.2 in Fig.…”

“…Breaking wave reciprocity in linear systems has been a growing focus of recent acoustic and elastic metamaterials research [22][23][24] . It has been shown that the induction of linear or angular motion, whether physically [25][26][27] or artificially [28][29][30] can instigate non-reciprocal wave propagation. On the realization front, some efforts have proposed the achievement of non-reciprocal systems via external stimulation of adaptive structures, e.g.…”

Surface wave non-reciprocity via time-modulated metamaterials

“…Similar considerations apply to locally-resonant metamaterials featuring an elastic wave-carrying medium equipped with a set of auxiliary resonators [20]. In this case, a wave-like modulation of the properties of the resonators causes the appearance of additional asymmetric features within the dispersion relation, such as bandgaps and veering points [17,[21][22][23][24]. Exciting a modulated metamaterial at specific frequencies leads to phenomena such as nonreciprocal wave filtering and frequency conversion of transmitted/reflected waves [21].…”

“…To simplify this expression, we pre-multiply it by e ihωmt ω m /(2π), where h is an arbitrary integer, and we integrate the result over the modulation period, from −π/ω m to π/ω m . This averaging procedure is a standard method to study the dynamics of systems with time-varying properties, and has been adopted by others in the context of modulated media [15,22,35]. Leveraging the orthogonality of harmonic functions, we drop the summation in n and obtain the following equation, valid for all values of h:…”

Frequency selective wave beaming in nonreciprocal acoustic phased arrays

“…A recent surge of research activity has shown that the intentional breakage of time-reversal symmetry instigates a nonreciprocal behavior in LTI systems which can unlock new opportunities in wave manipulation that were otherwise untapped. Such nonreciprocal systems have the potential to fuel the future of many fields ranging from elasticity [25][26][27] , acoustics [28][29][30][31] , and electromagnetics [32][33][34] , to natural hazard protection and quantum computations. In optics, there exists a few studies which investigate nonreciprocal wave behavior in antennas 35,36 , space-time phase modulated metasurfaces [37][38][39][40] , and real time multi-functional metasurfaces 41 .…”