Improved theoretical analysis and design guidelines of a two-degree-of-freedom galloping piezoelectric energy harvester

This paper presents an improved analysis of a two-degree-of-freedom (2DOF) galloping-based piezoelectric energy harvester (GPEH). First, an overview of the 2DOF GPEH, together with some discussions on its physical implementation, are presented. The theoretical model of the 2DOF GPEH is then developed. The analytical solutions are derived using the harmonic balance method. The dynamic behaviour of the 2DOF GPEH is predicted according to the solution characteristics. Moreover, the mode activation mechanism of the 2DOF GPEH is theoretically unveiled: depending on the system parameters; there may exist a single or multiple stable solutions which correspond to different vibration modes of the 2DOF GPEH. Subsequently, an equivalent circuit model of the 2DOF GPEH is established. Circuit simulations are performed to verify the analytical solutions. Case studies through detailed theoretical analysis and circuit simulation give in-depth insights into the dynamic behaviour of the 2DOF GPEH. It is demonstrated that by tuning the stiffness of the auxiliary oscillator, either the first or the second mode vibration of the 2DOF GPEH can be activated, resulting in completely different dynamic behaviours and energy harvesting performance. Finally, from the perspectives of reducing the cut-in wind speed and improving the voltage output, several design guidelines are provided.