Performance Correction for Cantilevered Piezoelectric Energy Harvesters Considering Nonuniform Electric Field in the Piezoelectric Layer

Through advances in wireless sensor networks and micro electro-mechanical systems over the past couple of decades, energy harvesting from the ambient environment as a self-sustaining energy source has attracted more and more attention worldwide. Piezoelectric materials are ideal sources for energy harvesting, since they can convert minor mechanical energy, which is often neglected or wasted, into electrical energy directly. The most commonly used piezoelectric energy harvesting structure is the cantilevered beam. Investigators around the world have made significant effort on the modeling of cantilevered piezoelectric energy harvesters. Throughout previous modeling of cantilevered piezoelectric energy harvesters, without exception, the electric field in the piezoelectric layer is considered as uniform as the potential difference between the electrodes divided by the thickness of the piezoelectric layer. However, based on the uniform electric field assumption, the divergence of the electric displacement, which represent the free charge density, in the piezoelectric layer is nonzero. This is against a basic physical law, i.e., the free charge in an insulator should be zero. By introducing the divergence of the electric displacement in the piezoelectric layer as zero, we found that the electric field in the piezoelectric layer is actually nonuniform. Using the electrical boundary conditions, the nonuniform electric field in the piezoelectric layer is derived and utilized in a distributed parameter model. Considering the present proposed nonuniform electric field, the theoretical performance of a cantilevered energy harvester is corrected. The proposed nonuniform electric field could also be applied to other bending piezoelectric components such as composite piezoelectric plates.