A distributed parameter electromechanical and statistical model for energy harvesting from turbulence-induced vibration

Extensive research has been done on the topics of both turbulence-induced vibration and vibration based energy harvesting; however, little effort has been put into bringing these two topics together. Preliminary experimental studies have shown that piezoelectric structures excited by turbulent flow can produce significant amounts of useful power. This research could serve to benefit applications such as powering remote, self-sustained sensors in small rivers or air ventilation systems where turbulent fluid flow is a primary source of ambient energy. A novel solution for harvesting energy in these unpredictable fluid flow environments was explored by the authors in previous work, and a harvester prototype was developed. This prototype, called piezoelectric grass, has been the focus of many experimental studies. In this paper the authors present a theoretical analysis of the piezoelectric grass harvester modeled as a single unimorph cantilever beam exposed to turbulent cross-flow. This distributed parameter model was developed using a combination of both analytical and statistical techniques. The analytical portion uses a Rayleigh–Ritz approximation method to describe the beam dynamics, and utilizes piezoelectric constitutive relationships to define the electromechanical coupling effects. The statistical portion of the model defines the turbulence-induced forcing function distributed across the beam surface. The model presented in this paper was validated using results from several experimental case studies. Preliminary results show that the model agrees quite well with experimental data. A parameter optimization study was performed with the proposed model. This study demonstrated how a new harvester could be designed to achieve maximum power output in a given turbulent fluid flow environment.