Experimental Observation of Nonreciprocal Band Gaps in a Space-Time-Modulated Beam Using a Shunted Piezoelectric Array

Abstract

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...

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

“…Among the key results, we demonstrate non-reciprocity associated with attenuation and amplification for waves propagating in different directions in 1D and 2D lattices, along with their topological properties associated with winding number of the complex dispersion bands, and localization of bulk modes at edges and corners. While idealized spring-mass lattices where used herein to elucidate the fundamental properties of elastic media with feedback interactions, we highlight that already existing platforms used to experimentally realize active materials with time-modulated properties [32][33][34][35][36] may potentially be modified to support feedback interactions of the type introduced here. The presented results open new possibilities for the design of active meta materials with novel functionalities such as those related to selective wave filtering, splitting, amplification and localization, both in one and two dimensions.…”

“…Topological states have been successfully observed in several platforms [13][14][15][16][17][18][19][20][21], and have been pursued to achieve robust, diffraction-free wave motion. Additional functionalities have been explored in the context of topological pumping [22][23][24][25][26], quasi-periodicity [27][28][29], and non-reciprocal wave propagation in active [30][31][32][33][34][35][36] or passive non-linear [37][38][39][40] systems. These works and the references therein illustrate a wealth of strategies for the manipulation of elastic and acoustic waves, and suggest intriguing possibilities for technological applications in acoustic devices, sensing, energy harvesting, among others.…”

Actively controllable topological phase transition in phononic beam systems

“…These surface electrodes are represented as brown and green rectangles in Fig. 1 [47] recently presented a similar structure, by using an experimental approach. They adopted the time-varying NCs to break the TR symmetry in an effort to realize non-reciprocal wave propagation.…”

Omindirectional Non-Reciprocity via 2D Modulated Radial Sonic Crystals

“…In this context, one dimensional space-time modulations have been successfully conceived to generate filtering bands (or bandgaps ) occurring at different frequencies for counter propagating waves. Topical examples of space-time modulation have been successfully realized in elastic structures through piezoelectric material with attached negative capacitance shunts [11,12]. Similarly, passive beams with embedded resonators have been used for this purpose, by properly phase shifting consecutive modulation signals, mimicking a plane wave propagation along the beam's dimension [13][14][15].…”