In this paper, we present a piezoelectric metamaterial integrated with bistable circuits to realize adaptive non-reciprocal elastic wave transmission. Dynamics of the bistable circuit and the piezoelectric metamaterial are investigated numerically to analyze the wave transmission characteristics of the proposed system. Results reveal that when the excitation amplitude exceeds certain threshold, wave energy is able to propagate even with excitation frequency inside the local-resonance bandgap of the piezoelectric metamaterial. This bandgap transmission phenomenon is also known as supratransmission. It is shown that by introducing spatial asymmetry, the system could exhibit different supratransmission thresholds when it is actuated in opposite directions, and hence there exists an excitation range within which wave energy is only able to propagate in one direction. Furthermore, this excitation range to facilitate non-reciprocal energy transmission is adaptable by adjusting the stable equilibria of the bistable circuits, which can be conveniently tuned utilizing only DC voltage sources. Additionally, it is shown that by adjusting the stable equilibria, the wave propagation direction, analogous to the forward direction of an electrical diode, can be easily reversed. Lastly, in contrast to many nonlinearity enabled non-reciprocal systems, the proposed system is able to realize non-reciprocal elastic energy transmission with majority of the transmitted energy preserved at the original input frequency. Overall, these results illustrate a new means of utilizing nonlinear piezoelectric metamaterial to manipulate elastic wave transmission.

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