Observation of nonreciprocal propagation for guided Lamb modes in piezoelectric phononic crystalsa).

Piezoelectric phononic-crystal plates, structured on their surface with metallic strips introducing electric-circuit loads, exhibit a tunable frequency-dispersion behaviour, nondestructively controlled in real time. Under an appropriate choice of boundary conditions through these loads, obeying a space-time propagation rule, it is demonstrated experimentally that these systems support nonreciprocal propagation of Lamb-like guided modes in their interior. The observations combined with numerical calculations confirm a broadband translation of the dispersion curves in the frequency-wavenumber space depending on the modulation speed. A careful analysis reveals a simple vector-rule relationship between the static bands and those induced by the time modulation of the external loads in the dispersion diagram. The device proposed in this study, offering dynamic changes in the electric boundary conditions by making use of switches driven by a microcontroller, thus, becomes an efficient tool not only for the realization of real-time control of elastic waves but also, and more importantly, a versatile platform for a robust generation of nonreciprocity effects in tunable, low-dimensional systems.