Non-reciprocal Wave Phenomena in Energy Self-reliant Gyric Metamaterials

Abstract

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 propagation 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.

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• Complex Spatiotemporal Modulations and Non-Hermitian Degeneracies in $\mathcal{P}\mathcal{T}$-Symmetric Phononic Materials
• Harnessing $\mathcal{P}\mathcal{T}$-symmetry in non-Hermitian stiffness-modulated waveguides
• Brillouin-zone definition in non-reciprocal Willis monatomic lattices
• Wave propagation in an elastic lattice with non-reciprocal stiffness and engineered damping
• Onset of wavenumber bandgaps via alternating Willis coupling signs
• A way to hypo-elastic artificial materials without a strain potential and displaying flutter instability