Electromechanical model of layered flexoelectric energy harvesters with strain gradient effect

Small size wireless devices entirely self-sufficient through energy harvesting from their local surroundings have wide applications. In this paper, an analytical model incorporating the effect of strain gradient for nanoscale flexoelectric energy harvesters is developed. The approximate closed-form solution of voltage output, which can provide a quick assessment of the efficiency of nanoscale flexoelectric energy harvesters, is provided. It is found that the optimal load resistance is not sensitive to the effects transverse shearing and strain gradient. For example, the optimal load resistances are 6.6 MΩ, 6.5 MΩ and 6.3 MΩ for the characteristic length scales are choses as 0 nm, 25 nm and 50 nm, respectively. The effect of transverse shearing on power output is more significant for a nanoscale flexoelectric energy harvester with smaller length to thickness ratio and larger proof mass. For example, power outputs predicted by Euler beam model are 17.6%, 3.8% and 0.06% higher than these predicted by Timoshenko beam model for the length to thickness ratios are 5, 10 and 20, respectively. In addition, the effect of strain gradient enhances the frequency therefore reduces the power output of the beam. The present model may be helpful for mechanical engineers and materials scientists for designing high-performance nanoscale flexoelectric energy harvesters.