A nonlinear model of a bimorph-based piezoelectric energy harvesting device

Energy harvesting devices provide an attractive approach to supplying an electrical energy source through the local conversion of mechanical energy from the surrounding environment. While a variety of applications, such as structural health monitoring and discrete actuation systems, may benefit from this technology, the use of energy harvesters in wireless sensor networks is considered here. The energy harvesting device converts mechanical energy to electrical energy through the use of a piezoelectric element. An attached circuit is also typically required to regulate the electrical output to a suitable source, although its role is not considered here. Instead, the focus of this research is to develop a model which can accurately predict the harvesting element's performance under a variety of conditions. The devices in question employ a common base element - a unimorph or bimorph annular disk. While a single element could form a complete harvester, devices typically use (and the model allows for) this base element with additional components, such as a proof mass or even multiple bimorph disks, which are connected in such a manner to match the device's resonance frequency with the expected drive frequency of the mechanical environment. Because of this versatility in its use, the development of a model to predict its performance is a critical step towards better understanding the device behavior and enabling the production of the next generation of energy harvesting devices. An assumed modes based model is developed using Lagrange's equations and expressions of the potential and kinetic energy, as well as the virtual work, of the harvesting device. With several physical characteristics of the device components and the selection of a set of assumed mode shapes, this method develops a discretized set of equations of motion for the harvesting device. Through several sets of experimental testing, the harvesting devices have exhibited nonlinear behavior and, as such, a nonlinearity is accommodated within the model through the use of a higher-order strain-displacement relation. This nonlinearity may be neglected, allowing for rapid computations of several device parameters, such as natural frequencies, mode shapes, and electro-mechanical coupling coefficients, as well as more complicated outputs such as frequency response functions. Of greater interest, however, are the nonlinear equations of motion. By time-integrating these equations, the nonlinearity exhibited by the devices can be further investigated. Through the comparison of model predictions and experimental data presented here, it is believed that the next generation of energy harvesting devices will be improved upon, either by eliminating the nonlinearity or by exploiting its presence, thus allowing for a greater energy harvesting performance.