Non-uniform electric field in cantilevered piezoelectric energy harvesters: An improved distributed parameter electromechanical model

In the existing electromechanical model for cantilevered piezoelectric energy harvesters, the electric field in the piezoelectric layer is generally considered as a uniform field. In the present study, it is found and described in detail that the oversimplified uniform electric field assumption could lead to critical issues regarding the fundamental of piezoelectricity. Further, inspired by the electric field distribution obtained using the exact solutions for plane problems, a non-uniform electric field is proposed. Accordingly, an improved distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters including both unimorph and bimorph configurations is established, in which the bending stiffness term involved in the electromechanical governing equations is explicitly corrected, and the aforementioned critical issues are perfectly addressed. The present proposed non-uniform electric field is then validated by comparing the static analysis results of the present model with finite element results and the results obtained using exact solutions for plane problems. Dynamic analysis of the present model is also conducted, and the electromechanical characteristic corrections for the traditional distributed parameter model adopting uniform electric field assumption is carried out including bending stiffness correction, resonant frequency correction, voltage output correction and power output correction.