Modeling and Characterization of Elastic, Coupling, and Dissipative Nonlinearities in PZT Bimorphs for Vibration Energy Harvesting

In numerous applications of lead zirconate titanate (PZT)-based devices, such as dynamic actuation, vibration control, sensing, and energy harvesting, inherent nonlinearities are inevitably pronounced for a broad range of mechanical and electrical excitation levels. Even in the absence of any geometric nonlinearity, researchers observed and reported nonlinear behavior in PZT-based devices for moderate-to-high excitation levels. Over the past two decades, the softening nonlinearities have been attributed to different phenomena by different research groups, such as purely elastic nonlinear terms and coupling nonlinearity. Dissipative effects of quadratic order have been observed but often attributed to air damping in symmetric structures. In an effort to develop a global nonlinear, non-conservative modeling framework, we combined elastic, coupling, and dissipative nonlinearities to explore primary resonance behavior in bimorph cantilevers for problems of mechanical and electrical excitation. We use this model to characterize the nonlinearities in piezoelectric bimorphs for energy harvesting with a focus on a symmetric brass-reinforced PZT-5A sample under base excitation. Specifically we point out the importance of quadratic nonlinearities in both stiffness and damping. Coupling and higher-order elastic nonlinearities from the electric enthalpy are observed to become effective only for the highest excitation levels close to physical limits of the device with high linear stiffness tested in this work.