Space-time-varying materials theoretically pledge to deliver non-reciprocal dispersion in linear systems by inducing an artificial momentum bias. Although such a paradigm eliminates the need for actual motion of the medium, experimental realization of space-time systems with dynamically changing material properties has been elusive. In this letter, we present an elastic metamaterial that exploits stiffness variations in an array of geometrically phase-shifted resonators -rather than external material stimulation -to induce a temporal modulation. We experimentally demonstrate that the resulting bias breaks time-reversal symmetry in the resonant metamaterial, and achieves a non-reciprocal tilt of dispersion modes within dynamic modulation regimes.

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In this paper, a physical platform is proposed to change the properties of phononic crystals in space and time in order to achieve nonreciprocal wave transmission. The utilization of magnetoelastic materials in elastic phononic systems is studied. Material properties of magnetoelastic materials change significantly with an external magnetic field. This property is used to design systems with a desired wave propagation pattern. The properties of the magnetoelastic medium are changed in a traveling wave pattern, which changes in both space and time. A phononic crystal with such a modulation exhibits one-way wave propagation behavior. An extended transfer matrix method (TMM) is developed to model a system with time varying properties. The stop band and the pass band of a reciprocal and a nonreciprocal bar are found using this method. The TMM is used to find the transfer function of a magnetoelastic bar. The obtained results match those obtained via the theoretical Floquet-Bloch approach and numerical simulations. It is shown that the stop band in the transfer function of a system with temporal varying property for the forward wave propagation is different from the same in the backward wave propagation. The proposed configuration enables the physical realization of a class of smart structures that incorporates nonreciprocal wave propagation.

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.

This work presents a generalized physical interpretation of unconventional dispersion asymmetries associated with moving phononic crystals (PCs). By shifting the notion from systems with time-variant material fields to physically traveling materials, the newly adopted paradigm provides a novel approach to the elastic dispersion problem and, in the process, highlights discrepancies between moving PCs and stationary ones with dynamic material fields. Equations governing the motion of an elastic rod with a prescribed moving velocity observed from a stationary reference frame are used to predict propagation patterns and asymmetries in wave velocities obtained as a result of the induced linear momentum bias. Three distinct scenarios are presented corresponding to a moving rod with a constant modulus, a spatially varying one, and one that varies in space and time. These cases are utilized to extract and interpret correlations pertaining to directional velocities, dispersion patterns, as well as nature of band gaps between moving periodic media and their stationary counterparts with time-traveling material properties. A linear vertical shear transformation is then derived and utilized to neutralize the effect of the moving velocity on the resultant band diagrams. Finally, dispersion contours associated with the transient response of a finite moving medium are used to validate the entirety of the presented framework.

This work presents a mechanism by which non-reciprocal wave transmission is achieved in a class of gyric metamaterial lattices with embedded rotating elements. A modulation of the device's angular momentum is obtained via prescribed rotations of a set of locally housed spinning motors and are then used to induce space-periodic, time-periodic, as well as space-time-periodic variations which influence wave propagations in distinct ways. Owing to their dependence on gyroscopic effects, such systems are able to break reciprocal wave symmetry without stiffness perturbations rendering them consistently stable as well as energy self-reliant. Dispersion patterns, band gap emergence, as well as non-reciprocal wave transmission in the space-time-periodic gyric metamaterials are predicted both analytically from the gyroscopic system dynamics as well as numerically via time-transient simulations. In addition to breaking reciprocity, we show that the energy content of a frictionless gyric metamaterial is conserved over one temporal modulation cycle enabling it to exhibit a stable response irrespective of the pumping frequency.

Elastic metamaterials utilize locally resonant mechanical elements to onset band gap characteristics that are typically exploited in vibration suppression and isolation applications. The present work employs a comprehensive structural intensity analysis (SIA) to depict the structural power distribution and variations associated with band gap frequency ranges, as well as outside them along both dimensions of a two-dimensional (2D) metamaterial. Following a brief theoretical dispersion analysis, the actual mechanics of a finite metamaterial plate undergoing flexural loading and consisting of a square array of 100 cells is examined experimentally using a fabricated prototype. Scanning laser Doppler vibrometer (SLDV) tests are carried out to experimentally measure the deformations of the metamaterial in response to base excitations within a broad frequency range. In addition to confirming the attenuation and blocked propagation of elastic waves throughout the elastic medium via graphical visualizations of power flow maps, the SIA reveals interesting observations, which give additional insights into energy flow and transmission in elastic metamaterials as a result of the local resonance effects. A drastic reduction in power flow magnitudes to the bulk regions of the plate within a band gap is noticeably met with a large amplification of structural intensity around and in the neighborhood of the excitation source as a compensatory effect. Finally, the theoretical and experimentally measured streamlines of power flow are presented as an alternative tool to predict the structural power patterns and track vortices as well as confined regions of energy concentrations.