Energy harvesting properties of the functionally graded flexoelectric microbeam energy harvesters

Abstract

Flexoelectricity may be an excellent candidate for piezoelectricity in micro and nano scaled energy harvesters due to its strong size dependency. In this paper, a size dependent analytical model of the cantilever-based functionally graded flexoelectric energy harvesters is developed. The Hamilton's principle is used to derive the governing equations. By means of the Galerkin's method, the approximated closed-form solutions of electrical output and energy conversion efficiency are obtained. For the functionally graded flexoelectric energy harvester, the effective flexoelectric response is controlled by not only the flexocoupling coefficient but also its first derivative. Numerical results of a 3 μm-thick Polyvinylidene Fluoride/Strontium Titanate composed functionally graded flexoelectric energy harvester demonstrate that when the volume fraction exponent varies from zero to infinity, the optimal working frequency gradually reduces from 41407 Hz to 7761 Hz and the optimal load resistance gradually increases from 0.99 MΩ to 83.91 MΩ. Meanwhile, shrinking the thickness from 3 μm to 0.3 μm will highly increase the normalized power density and the energy conversion efficiency about one and two orders, respectively. Moreover, when the strain gradient elastic coefficient becomes larger, the natural frequency will increase while the corresponding maximum electrical output will decrease.