Surface integrity and size dependent modeling and performance of non-uniform flexoelectric energy harvesters

Piezoelectric energy harvesters have recently been the focus of several researchers over several years due to their effectiveness at submicron scales by including the flexoelectric effect. Though the size-dependency of the flexoelectric effect had been examined at nanoscales, the size dependent effects of the material structure had been neglected; these nanoscale models do not accurately represent models at the nanoscale. A robust reduced-order model is introduced in this study that incorporates material structure size-dependency through the couple stress theory, the effects of the surface profile by examining the average roughness and slope of roughness and the impacts of the surface stress through the Gurtin-Murdoch surface elasticity theory on a non-uniform cantilever beam energy harvester. Couple stress considerations greatly impact all examined systems, harden the system, and increase the power bandwidth whereas surface roughness influences the expected harvestable power and optimal loading of the system, by reducing expected power output. This analysis shows the importance of considering the size dependent effects on the performance of flexoelectric energy harvesters in nanoscale.