Modelling of Vibration Sensor Based on Bimorph Structure

In the current study, we have developed a mathematical model describing the frequency response of a sensor or energy harvester based on a cantilever made of a ferroelectric bidomain single-crystal plate with metal electrodes deposited on opposite faces. The structure is subjected to vibrational excitations. The model allows to predict the dependence of the voltage between the electrodes vs. the vibration frequency and amplitude as well as resonance frequency of the sensor fabricated in form of a rectangular plate, normally with a seismic mass on its free end. The device is placed on a vibration table, whose vibration parameters are set. The relevant differential equation was composed, and an analytic solution describing the required dependencies was obtained. To validate the proposed model, we created a single-crystal bimorph by annealing a lithium niobate (LiNbO₃) wafer in air to promote Li out-diffusion and formation of a bidomain ferroelectric structure, i.e. two oppositely polarized domains within the plate (the so called “head-to-head” structure). Such a crystal demonstrates a bimorph-like behavior but does not comprise any interface except for an interdomain wall. Thus, our bimorph is not a commonly used structure, typically consisting of two bonded piezoelectric plates (generally made of PZT piezoceramics), but a homogeneous continuous medium. Being made of a lithium niobate (or lithium tantalate) ferroelectric single crystal, the cantilever sensor or energy harvester demonstrates a strong dependence of the voltage between the electrodes on the bending deformations, with almost totally absent hysteresis and ageing in a wide temperature range. The comparison made between the results of the modeling and the experiment shows that the proposed model is in good agreement with the experiment. We have demonstrated that the vibration sensors based on bidomain single-crystal plates possess an exceptionally high sensitivity. The proposed model can be used to estimate and predict the parameters of vibration sensors, accelerometers and waste energy harvesters based on bidomain ferroelectric crystals.