Analysis of an array of flexoelectric layered nanobeams for vibration energy harvesting

Abstract

Comparing with a single energy harvester, an array of energy harvesters can provide higher electrical power output and wider frequency bandwidth. In this article, with consideration of surface effect, an array of layer flexoelectric nanobeams with proof mass connected in parallel and/or series are investigated. Governing equations are derived based on the Hamiltonian principle. Reduced order models for both parallel and series systems are obtained. Closed-form expressions for voltages are presented. Results show that the power, the frequency and the optimal resistances of the system are dependent of surface effect. The flexoelectricity has more significant effect on the normalized power however its effect on the frequency and the optimal resistances can be ignored. The optimal resistance of the system depends on surface effect, the number of array elements and its circuits. Moreover, increasing proof mass delivers a wider bandwidth at the cost of peak normalized power. The peak normalized voltage and power of the parallel system is small than those of the series system, but the bandwidth of the two systems is the same. This is important information for the design of an array of flexoelectric energy harvesters.