Modeling and verification of piezoelectric wind energy harvesters enhanced by interaction between vortex-induced vibration and galloping

Previous works verified experimentally that interactions between vortex-induced vibration (VIV) and galloping may greatly improve the performance of piezoelectric wind energy harvesters (PWEHs) at low wind speeds. However, no mathematical model has been available to date to predict the responses or optimize the structures of PWEHs. In this paper, a distributed-parameter electromechanical coupling model of a VIV-galloping interactive PWEH was derived and was then experimentally validated using two harvester prototypes. For the first prototype, while the theoretical critical galloping speed is approximately 2.1 times the theoretical critical VIV speed, the experiments verified the proposed model's prediction that this harvester involves full interaction between VIV and galloping because there is only one wind speed region (in the wind speed range of interest) that offers high electrical output. For the second prototype, whose theoretical galloping speed is about 2.3 times the critical VIV speed, the model indicates that there are two completely separate wind speed regions that have relatively high electrical outputs, implying that this is a harvester without the interaction between VIV and galloping, coinciding with the experimental results. For both prototypes, the model is accurate enough to predict the onset reduced speeds for the wind speed regions with high electrical outputs, and can be used to obtain the output voltage in the wind speed range of interest. The proposed model can thus be used to design VIV-galloping interactive PWEHs with enhanced performance in the collection of low speed airflows.