Theoretical Analysis Of D₃₁ Mode Cantilevered Piezoelectric Transducer Actuation And Energy Harvesting Performance

Because of the maturity of micro-electromechanical systems (MEMS) techniques, thetraditional piezoelectric transducer is toward the development of miniaturization andintegration, its application such as high speed atomic force microscopy, nanoscaleelectromechanical switches, resonators, radio-frequency flters, biosensors and energyharvester, etc. Therefore the piezoelectric transducers fabricated by using of MEMStechniques are paid close attention of the domestic and overseas scientific researchers.Among the piezoelectric transducers, the1-3mode of operation has become the hot topic ofresearch, because its process is relatively simple and its actuation and energy harvestingperformances are superior. Although many theoretical models are set up for the1-3modepiezoelectric transducers, the modeling of the multilayered micro-cantilevered structure isseldom reported. The research object of this thesis is the1-3mode cantileveredpiezoelectric transducers. In this thesis, we set up a dynamic model of the multilayeredcantilevered piezoelectric actuator combining the piezoelectric constitutive equations andEuler-Bernoulli beam theory, and the analytical expressions of the deflection and outputvoltage are derived for the cantilevered piezoelectric bimorph operated at harmonicexcitations based on Timoshenko beam theory. The theoretically calculated results arecompared with the experimental and the finite element simulation results to verify theproposed model validity. The main contents and results of this thesis are given as follows:1. Based on Euler-Bernoulli beam theory without considering the residual stresses onthe micro-cantilevered piezoelectric actuator (MCPA), a multilayered MCPA model is set upwith considering the buffer layer and electrodes. The first mode resonance frequency-beamlength, the tip deflection-voltage and harmonic response curves are simulated by using thetraditional and proposed models, and the results based on the proposed model are muchcloser to the experimental and finite element simulation results than those based on thetraditional model, indicating that the proposed model is valid for evaluating the actuationperformances of the MCPA. The effect of the mechanical damping and bending stiffness onthe actuation performance of the MCPA is also discussed. Using the proposed model, thedependences of the frst-mode resonance frequency and tip defection of the MCPA onnon-piezoelectric layer thicknesses are analyzed at the certain driving voltage.2. Combining the piezoelectric constitutive equations of d31mode with the Timoshenkobeam model, we set up an electromechanical model of the cantilevered piezoelectric bimorph energy harvester in series connection. The output voltage-excitation frequency andoutput power-excitation frequency curves based on the proposed model are very close tothose of the experiment, and indicating that the proposed model may evaluate exactly theoutput responses and the frequency shifts due to load resistance changing of thecantilevered piezoelectric bimorph. Further, the output peak voltage-load resistance, theoutput peak power-load resistance curves are also simulated by the proposed model andresults indicate again that the proposed model may exactly predict the energy harvestingperformances of the cantilevered piezoelectric bimorph.3. We have designed the segmented and un-segmented electrodes MCPAs with(Na0.85K0.15)0.5Bi0.5TiO3ferroelectric thin film as the piezoelectric layer. Based on themulti-layered MCPA model in Chapter2, the tip deflection of the segmented andun-segmented electrode MCPAs are simulated under the alternating current driving voltage.The results indicate that the tip deflection of the segmented electrode MCPA is twice largerthan the un-segmented for the second mode. Meanwhile, we have also set up a static modelof the segmented electrode MCPA to evaluate the static output tip deflection and force ofthe segmented electrode structure MCPA.