Predictive Electromechanical Model for Energy Scavengers Using Patterned Piezoelectric Layers

Abstract

The piezoelectric transduction mechanism is widely used in passive sensing, health monitoring, and energy harvesting. Plate-type energy harvesters are usually discouraged; however, piezoelectric layers on a substrate in a certain pattern were found to be suitable for harvesting energy from a wider band of frequencies. However, to understand the theoretical behavior of the harvesters with any arbitrarily shaped piezo patch, a detailed mathematical model is lacking. This paper proposes a comprehensive analytical model to calculate the frequency response function (FRF) from simply patterned piezoelectric layers. A generalized mathematical form is presented for an arbitrary rectangular piezoelectric patch placed on a host plate. The strain-rate damping mechanism is incorporated for better and more accurate results. First, a comparative study on the strain-rate damping effect is presented by placing the piezoelectric layer on the entire plate. Without strain-rate damping, the model incorrectly estimates voltage output. Further, a methodology through a genetic algorithm optimization process is proposed to generate the required pattern of piezoelectric layers tailored to a desired requirement. With the proposed generalized mathematical model, the voltage output from the harvester with any particular shape and size of piezoelectric layers can be calculated predictively.