In this work we experimentally achieve 1 kHz-wide directional band-gaps for elastic waves spanning a frequency range from approximately 8 to 11 kHz. One-way propagation is induced by way of a periodic waveguide consisting in an aluminum beam partially covered by a tightly packed array of piezoelectric patches. The latter are connected to shunt circuits and switches which allow for a periodic modulation in time of the cell properties. A traveling stiffness profile is obtained by opportunely phasing the temporal modulation of each active element, mimicking the propagation of a plane wave along the material, therefore establishing unidirectional wave propagation at bandgap frequencies.Nonreciprocal devices have been pursued in various research domains and physical platforms, including quantum [1], electromagnetic [2,3], acoustic [4][5][6] and elastic [7-9] media. These devices support wave propagation from a point (A) to one other (B), but not vice-versa, opening up new possibilities for the control of energy flow with unprecedented performance in communication systems [10], unidirectional insulators [11] and converters [12,13], among others. Important contributions in the context of one-way phonon transport have been formulated by Fleury et. al. [14,15], demonstrating directional wave manipulation in acoustic cyrculator devices. Also, elastic and acoustic directional waveguides have been conceived and physically realized, in analogy with the Quantum Hall effect (QHE), achieving backscattering immune and one-way topological edge states [16][17][18][19][20]. Other approaches to nonreciprocity leverage nonlinear phenomena [21,22], metastability [23], bifurcation and chaos [24] which are particularly attractive solutions due to the presence of solely passive elements. However, the exploitation of nonlinear dynamics usually requires high wave amplitudes, thus making the physical realization impractical for compact devices. An effective platform to break reciprocity is offered by space-time modulated systems [25,26]. Notable recent examples have employed programmable magnetic lattice elements [27] and magnetic springs [28]. In this work we experimentally investigate nonreciprocity in a phononic beam, where spatial and temporal modulations are induced upon electric control of equivalent elastic properties. Namely, the spatial modulation is induced by bonding a pattern of piezoelectric elements on a passive substrate, which effectively alter the Young-s modulus of the waveguid through negative capacitance shunts [29], which are manipulated in time through a switching logic. This enables the formation of a traveling stiffness profile, which produces an asymmetric dispersion relation, which is a hallmark of nonreciprocity.As shown in [29], the proposed configuration an effective mean to test non-reciprocity of spatio-temporally modulated media, and may also be adopted as a flexible platform to explore other phenomena associated with temporal and spatio-temporal modulation, among which parametric amplification [29], conversi...

We demonstrate that modulations of the stiffness properties of an elastic plate along a spatial dimension induce edge states spanning non-trivial gaps characterized by integer valued Chern numbers. We also show that topological pumping is induced by smooth variations of the phase of the modulation profile along one spatial dimension, which results in adiabatic edge-to-edge transitions of the edge states. The concept is first illustrated numerically for sinusoidal stiffness modulations, and then experimentally demonstrated in a plate with square-wave thickness profile. The presented numerical and experimental results show how continuous modulations of properties may be exploited in the quest for topological phases of matter. This opens new possibilities for topology-based waveguiding through slow modulations along a second dimension, spatial or temporal.

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We experimentally demonstrate that a rainbow-based metamaterial, created by a graded array of resonant rods attached to an elastic beam, operates as a mechanical delay-line by slowing down surface elastic waves to take advantage of wave interaction with resonance. Experiments demonstrate that the rainbow effect reduces the amplitude of the propagating wave in the host structure. At the same time, it dramatically increases both the period of interaction between the waves and the resonators and the wavefield amplitude in the rod endowed with the harvester. Increased energy is thus fed into the resonators over time: we show the enhanced energy harvesting capabilities of this system.

In this paper, we report the evidence of topologically protected edge waves (TPEWs) in continuum Kagome lattice. According to the bulk edge correspondence principle, such edge states are inherently linked with the topological characteristics of the material band structure and can, therefore, be predicted evaluating the associated topological invariant. Due to the non-trivial band structures shown in the context of quantum valley Hall effect, TPEWs are supported at the interface between two lattices characterized by different valley Chern numbers. The break of lattice symmetry is obtained here, in contrast with other similar works in continuum elastic structures, biasing in the stiffness properties of the unit cell, instead of manipulating mass at sublattice points. This opens new promising possibilities related to waveguide tunability and wave propagation control, exploiting the established techniques for stiffness modulation in elastic structures. A sensitivity analysis of robustness of the supported energy transport is provided, showing the amount of de-localized disorder the waveguide is immune to, and how performances are affected by perturbations in the nominal parameters of the lattice.

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