A low-order model for the design of energy harvesting piezoelectric devices

The use of energy harvesting devices is an attractive method of utilizing available mechanical energy by converting it into usable electrical energy. Numerous potential applications exist for energy harvesting devices, including structural health monitoring, discrete actuation systems, and wireless sensor networks, which are considered here. A piezoelectric element is employed to convert mechanical energy from a vibration environment to electrical energy, which is then converted to a regulated power source through an attached circuit. While the devices considered vary in configuration, the essential component is the piezoelectric unimorph or bimorph annular plate with an associated proof mass designed to be mechanically driven near its resonance frequency. The development of a low-order model is a critical step in predicting the device behavior for both the current and future generations of devices. Such a model, based on the assumed modes method, is developed and presented. As employed here, the assumed modes method uses Lagrange's equations and a computation of the (both electrical and mechanical) potential and kinetic energy and virtual work of the device. The model provides a rapid computation of key parameters such as open- and short-circuit natural frequencies, device coupling coefficient, and mode shapes for a device of circular geometry, as well as the ability to produce frequency response functions and time-varying responses to arbitrary forcing functions. Model predictions are compared with experimental data and the model is also used to analyze various physical connections of such plates in a manner like component mode synthesis. A particular strength of the model is the ease with which device parameters, such as the piezoelectric element thickness or device radius, can be changed to evaluate their impact on the device performance. As such, the model is useful when designing the next generation of devices or optimizing a particular configuration, an example of which is presented.