Engineering nonreciprocal wave dispersion in a nonlocal micropolar metabeam

Abstract

Active metamaterials with electronic control schemes can exhibit nonreciprocal and/or complex elastic coefficients that result in non-Hermitian wave phenomena. Here, we investigate theoretically and experimentally a non-Hermitian micropolar metabeam with piezoelectric elements and electronic nonlocal feed-forward control. Since the nonlocal feed-forward control breaks spatial reciprocity, the proposed metabeam supports nonreciprocal flexural wave propagation, featuring unidirectional amplification/attenuation and non-Hermitian skin effect. Theoretical homogenization modeling is developed to consider the nonlocal effect into an effective complex bending stiffness. The unidirectional wave amplification/attenuation is attributed to the energy conversion between electrical power and mechanical work. The non-Hermitian skin effect, characterized by a winding number, is the manifestation of the flexural nonreciprocity and admits an extensive number of localized bulk eigenmodes on open boundaries. The nonlocal metabeam is also employed to engineer the anomalous wave dispersion such as tunable roton-like dispersion and band tilting. The nonlocal micropolar metabeam could pave the ways for designing non-Hermitian topological mechanical metamaterials featuring programmable nonreciprocal wave transmission and engineering roton-like wave dispersion relations under ambient environments.

Observation of Chirality‐Induced Roton‐Like Dispersion in a 3D Micropolar Elastic Metamaterial

“…These overall results represent a chiral route to roton-like dispersions of the lowest band that is complementary to a different previous (achiral) route based on third-nearest-neighbor interactions. [38][39][40][41][42][43][44] There, rotons have resulted from the ultrastrong coupling and hybridization of two different acoustical phonon modes. [34][35][36] Here, rotons result from the ultrastrong coupling and hybridization of optical and acoustical phonon branches.…”

Cubic-symmetry acoustic metamaterials with roton-like dispersion relations

“…There, the dispersion relation starts with frequency being proportional to wavenumber. For larger wavenumbers, frequency exhibits a maximum, followed by a region of negative slope and a minimum, which is referred to as the roton [14][15][16][17][18][19][20][21][22][23] . The region of negative slope corresponds to backward waves over a large relative bandwidth, i.e., to a situation for which the phase velocity is opposite to the group velocity.…”

Dispersion Engineering by Hybridizing the Back‐Folded Soft Mode of Monomode Elastic Metamaterials with Stiff Acoustic Modes

“…[4][5][6] Numerous further types of avoided crossing have been discussed in the literature. [7,8] Recently, the hybridization of different photon modes [9] or phonon [11][12][13][14][15][16][17][18] modes has been exploited to realize dispersion relations resembling the roton dispersion relation of sound in liquid helium-4. [19] This dispersion relation contains a broad region of backward waves, for which group velocity and phase velocity have opposite signs, indicating a negative refractive index.…”