Multi-electrode piezoelectric plates as non-reciprocal metamaterials

Abstract

Non-reciprocal transmission of elastic waves through a solid is an exciting phenomenon that could open up new applications for elastic metamaterials. Non-reciprocal transmission of elastic waves can be achieved with spatio-temporally modulated boundary conditions. Some previous studies of non-reciprocal metamaterials have used uniformly modulated piezoelectric patches on metal host beams. Those beams have the advantage of electrically tunable boundary conditions due to the electro-mechanical coupling in piezoelectric patches, but are multi-material composites that are not easy to scale down. Instead, we show multi-electrode (patterned) piezoelectric plates, which are practical for a large range of geometric scales and frequencies, can exhibit non-reciprocal transmission with spatio-temporally modulated shunted circuits connected to the electrodes. In this work a study of sub-wavelength, ultrasonic band gaps that arise from shunted circuits on piezoelectric plates will be presented. The achievement of spatio-temporal modulation by using time-modulated capacitor-inductor circuits that vary in phase with their neighbors will be discussed. The results of frequency domain simulations of non-reciprocal transmission will be presented, and future directions for this research will be discussed. [Work funded by the Office of Naval Research.]