Optimal electrode coverage based on a new criterion for piezoelectric energy harvesters

Piezoelectric energy harvesters (PEHs) are a promising alternative to conventional electrochemical batteries with the advantage of being self-powered and maintenance-free, but their application is severely restricted by the low electric power output. It has been reported that the power output of PEHs can be enhanced by well-designed electrode coverage. A common design criterion for beam-like PEHs is based on the strain node to avoid electrode charge cancellation. This criterion, however, is not feasible for PEHs subject to complex spatio-temporal excitation patterns, where strain nodes change their position. This work proposes a new design criterion for optimal electrode coverage of beam-like PEHs based on the closed-form solution of the circuit equation that expresses voltage as a function of the beam's dynamic response, specifically the cross-section rotation. The new criterion maximizes the averaged curvature of the beam segment covered by the electrode using data on the instantaneous rotation field. The improved physical significance and reliability of the presented criterion are discussed. The associated electrode optimization procedure is then exemplified for PEHs driven by fluid flow, which helps to realize a complex excitation pattern. Two numerical studies, both including a variety of combinations of fluid densities and inlet velocities, are performed to demonstrate that an optimal electrode configuration can be obtained with the proposed criterion. Comparison of different electrode configurations in above studies finally leads to useful conclusions on the power output and electrode configuration.