Performance Correction and Parameters Identification Considering Non-Uniform Electric Field in Cantilevered Piezoelectric Energy Harvesters.

In the current electromechanical model of cantilevered piezoelectric energy harvesters, the assumption of uniform electric field strength within the piezoelectric layer is commonly made. This uniform electric field assumption seems reasonable since the piezoelectric layer looks like a parallel-plate capacitor. However, for a piezoelectric bender, the strain distribution along the thickness direction is not uniform, which means the internal electric field generated by the spontaneous polarization cannot be uniform. In the present study, a non-uniform electric field in the piezoelectric layer is resolved using electrostatic equilibrium equations. Based on these, the traditional distributed parameter electromechanical model is corrected and simplified to a practical single mode one. Compared with a traditional model adopting a uniform electric field, the bending stiffness term involved in the electromechanical governing equations is explicitly corrected. Through comparisons of predicted power output with two-dimensional finite element analysis, the results show that the present model can better predict the power output performance compared with the traditional model. It is found that the relative corrections to traditional model have nothing to do with the absolute dimensions of the harvesters, but only relate to three dimensionless parameters, i.e., the ratio of the elastic layer's to the piezoelectric layer's thickness; the ratio of the elastic modulus of the elastic layer to the piezoelectric layer; and the piezoelectric materials' electromechanical coupling coefficient squared, k312. It is also found that the upper-limit relative corrections are only related to k312, i.e., the higher k312 is, the larger the upper-limit relative corrections will be. For a PZT-5 unimorph harvester, the relative corrections of bending stiffness and corresponding resonant frequency are up to 17.8% and 8.5%, respectively. An inverse problem to identify the material parameters based on experimentally obtained power output performance is also investigated. The results show that the accuracy of material parameters identification is improved when considering a non-uniform electric field.