Design and experimental analysis of nonreciprocal wave propagation in a space-time modulated beam

Breaking reciprocity in wave propagation problems is of great interest within the research community, given the opportunity to design new devices for one-way communication with unprecedent performances. In the context of mechanics and phonon transport, directional wave manipulation can be achieved exploiting space-time periodic materials. Namely, structures whose elastic or physical properties are functions of space and time. In this work we experimentally study nonreciprocal wave propagation in a space-time modulated beam based on piezoelectric actuation. The system is made of an aluminum beam with an array of piezoelectric patches bonded on its top and bottom surface. Each patch is attached to a negative capacitance (NC) shunt driven by switching circuit, which is able to provide a square-wave stiffness profile in time to the layered material. Spatiotemporal modulation is induced by phase shifting the temporal modulation law of three consecutive piezo-elements, generating a traveling Young's modulus that mimics the propagation of a wave along the beam dimension. As a result, we achieved 1kHz directional bandgaps, i.e. bandgaps at different frequencies for counter propagating waves, which can be moved in a range spanning 8-11 kHz.