Programmable piezoelectric phononic crystal beams with shunt circuits: A deep learning neural network-assisted design strategy for real-time tunable bandgaps

A deep learning neural network-assisted design strategy for programmable piezoelectric phononic crystal (PnC) beams with shunt circuits is proposed. The feasibility of integrating deep learning into the design of tunable PnCs to achieve real-time vibration isolation is demonstrated through numerical examples. The influence of shunt circuits (capacitance) on bandgaps of piezoelectric PnCs is studied by finite element (FE) simulations. The results show that the bandgap frequency and range vary with the capacitance and electrode length. Moreover, incorporating supercell structures introduces an additional bandgap, significantly expanding the tunable range of the bandgap and demonstrating that shunt circuit modifications can tailor the frequency and width of the bandgap. A suite of deep learning neural network (NN) algorithms is developed for predicting bandgaps and inversely designing PnC parameters, greatly accelerating the bandgap calculation and enabling faster inverse design than existing models. The accuracy of the NN algorithms is verified by comparing their predictions with those from FE simulations. The combination of designed PnC beams and deep learning NNs enables real-time vibration reduction and isolation. This design strategy is successfully validated in a practical scenario involving real-time vibration isolation of train rails.