Electromechanical Modeling of Piezoelectric Energy Harvesters
Vibration-based energy harvesting has been investigated by several researchers over the last decade. The ultimate goal in this research field is to power small electronic components (such as wireless sensors) by using the vibration energy available in their environment. Among the basic transduction mechanisms that can be used for vibration-to-electricity conversion, piezoelectric transduction has received the most attention in the literature. Piezoelectric materials are preferred in energy harvesting due to their large power densities and ease of application. Typically, piezoelectric energy harvesters are cantilevered structures with piezoceramic layers that generate alternating voltage output due to base excitation. This work presents distributed-parameter electromechanical models that can accurately predict the coupled dynamics of piezoelectric energy harvesters. First the issues in the existing models are addressed and the lumped-parameter electromechanical formulation is corrected by introducing a dimensionless correction factor derived from the electromechanically uncoupled distributed-parameter solution. Then the electromechanically coupled closed-form analytical solution is obtained based on the thin-beam theory since piezoelectric energy harvesters are typically thin structures. The multi-mode electromechanical frequency response expressions obtained from the analytical solution are reduced to single-mode expressions for modal vibrations. The analytical solutions for the electromechanically coupled voltage response and vibration response are validated experimentally for various cases. The single-mode analytical equations are then used for deriving closed-form relations for parameter identification and optimization. Asymptotic analyses of the electromechanical frequency response functions are given along with expressions for the short-circuit and the open-circuit resonance frequencies. A simple experimental technique is presented to identify the optimum load resistance using only a single resistor and an open-circuit voltage measurement. A case study is given to compare the power generation performances of commonly used monolithic piezoceramics and novel single crystals with a focus on the effects of plane-stress material constants and mechanical damping. The effects of strain nodes and electrode configuration on piezoelectric energy harvesting are discussed theoretically and demonstrated experimentally. An approximate electromechanical solution using the assumed-modes method is presented and it can be used for modeling of asymmetric and moderately thick energy harvester configurations. Finally, a piezo-magneto-elastic energy harvester is introduced as a non-conventional broadband energy harvester.