Mathematical Modeling of an Active-Fiber Composite Energy Harvester with Interdigitated Electrodes

Abstract

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.

Modeling and parametric analysis of a unimorph piezocomposite energy harvester with interdigitated electrodes

“…cross section is zero and neglect the effect of the voltage across the electrodes. These positions are given by [25] as follows:…”

“…The developed model successfully predicted the dynamics of the MFC unimorph design especially for low values of electrical resistance load. Jemai et al [25] developed an analytical and numerical model for a unimorph AFC harvester. They assumed unidirectional and uniform electric field between successive electrodes in the case of relatively large electrode separation and small electrode's width.…”

“…Nevertheless, in most of the above mentioned studies where analytical solutions based on the Galerkin procedure are proposed, the presence of the piezoelectric patch is not taken into account to extract the mode shapes of the PVEH, either for the IDE configuration [24,25] or for the classical parallel electrode configuration [27,28,29]. In fact, often the calculated mode shapes incorrectly assume that the substrate beam is fully covered by the piezoelectric patch.…”

“…In this study, an improvement of the analytical model found in [25] is proposed along with an extensive parametric analysis of the system's geometric and physical properties that influence the harvested electrical energy. First, the exact mode shapes are considered by taking into account the non-uniform beam thickness.…”

“…Second, the proposed model accounts for non-uniform electric field between two consecutive IDE. Indeed, classical models of IDE harvesters consider only a uniform electric field that not only violates the Maxwell's equations but are also in conflict with numerical simulations done by FEM [21,22,25]. The derived analytical model and the obtained closed-form solutions are used to investigate the effects of various parameters on the harvested electrical power.…”