SUMMARY

This work is centered on the modeling, experimental identification, and dynamic interaction of inherently present and intentionally designed nonlinearities of piezoelectric structures focusing on applications to vibration energy harvesting. The following topics are explored in this theoretical and experimental research: (1) Frequency bandwidth enhancement using a simple, intentionally designed, geometrically nonlinear M-shaped oscillator for low-intensity base accelerations; (2) multi-term harmonic balance analysis of this structure for primary and secondary resonance behaviors when coupled with piezoelectrics and an electrical load; (3) inherent electroelastic material softening and dissipative nonlinearities for various piezoelectric materials with a dynamical systems approach; and (4) development of a complete approximate analytical multiphysics electroelastic modeling framework accounting for material, dissipative, and strong circuit nonlinearities. The ramifications of this research go well beyond energy harvesting, since inherent nonlinearities of piezoelectric materials are pronounced in various applications ranging from sensing and actuation to their combined use for vibration control, while intentional bandwidth enhancement impacts not only on energy harvesting but also vibration damping. Over the past two decades, similar manifestations of softening nonlinearity in piezoelectric materials have been attributed to different phenomena, such as purely elastic nonlinear terms and coupling nonlinearity, by different research groups. In order to develop a unified nonlinear non-conservative framework with two-way coupling, the nonlinear dynamic behavior of bimorph piezoelectric cantilevers under low-to-moderate mechanical and electrical excitation levels are explored in energy harvesting, sensing, and actuation, well below the coercive field. The resulting nonlinear non-conservative distributed-parameter electroelastic modeling framework is analyzed extensively using the method of harmonic balance for model validation and nonlinear parameter identification. This multi-term harmonic balance framework is then combined with other nonlinear effects such as strong circuit nonlinearities due to AC-DC conversion, and it can readily be extended to combining various nonlinear effects in other scenarios.