Mathematical modeling of an active-fiber composite energy harvester with interdigitated electrodes

The use of active-fiber composites (AFC) instead of traditional ceramic piezoelectric materials is motivated by flexibility and relatively high actuation capacity. Nevertheless, their energy harvesting capabilities remain low. As a first step toward the enhancement of AFC's performances, a mathematical model that accurately simulates the dynamic behavior of the AFC is proposed. In fact, most of the modeling approaches found in the literature for AFC are based on finite element methods. In this work, we use homogenization techniques to mathematically describe piezoelectric properties taking into consideration the composite structure of the AFC. We model the interdigitated electrodes as a series of capacitances and current sources linked in parallel; then we integrate these properties into the structural model of the AFC. The proposed model is incorporated into a vibration based energy harvesting system consisting of a cantilever beam on top of which an AFC patch is attached. Finally, analytical solutions of the dynamic behavior and the harvested voltage are proposed and validated with finite element simulations.