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.

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This study investigates the derivation of an accurate parameterized analytical model of a vibration-based energy harvester using piezocomposite material and interdigitated electrode. The derived model is used to analyze and optimize the harvested electrical energy under different resistance loads and excitation frequencies. The energy harvester is composed of a unimorph design cantilever beam partially covered by a piezocomposite material with interdigitated electrodes. The model provides an improved approach to optimize the performance of the system by taking into account the nonlinear electrical potential distribution and nonuniform vibration mode shapes over the beam's length due to the presence of the piezocomposite patch. We use a Galerkin procedure along with the Gauss's law to derive the analytical reduced-order model and study the dynamic response of the energy harvesting system. We demonstrate that different parameters are involved into the optimization process of the system such as the number of electrodes, the different layer thicknesses, the piezocomposite patch length, the fiber volume fraction and the substrate material. The proposed analysis shows that significant increase of the harvested energy could be obtained if all design parameters are correctly chosen. A numerical finite element model is also developed to validate the obtained analytical results.