Modeling of functionally graded circular energy harvesters due to flexoelectricity

Flexoelectric effect can be enhanced in micro/nano scale due to its size-dependency, making it particularly suitable for energy harvesting. In this work, a theoretical model is built to characterize the functionally graded circular flexoelectric energy harvesters based on the Kirchhoff thin plate hypothesis. Using Hamilton's principle, both the force balance equation and current balance equation are obtained. Approximated closed-form solutions of the energy harvesting performances are achieved through the assumed-mode method. Numerical analysis results demonstrate that the clamped circular energy harvesters with the ratio of the electrode radius to the plate radius be 0.64 will generate the maximum electrical output. The volume fraction coefficient has a significant impact on the resonant frequency, electrical output as well as the optimal load resistance. Meanwhile, shrinking the thickness of the circular energy harvester from 10µm to 0.1µm will lead to a remarkable increase of the optimal energy conversion efficiency from 10⁻⁶ to 10⁻². Furthermore, the strain gradient effect is examined to result in a higher resonant frequency while suppress the electrical output particularly if the length scale parameter is relatively large.