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 energy harvesting. The following topics are explored both theoretically and experimentally: (1) Inherent electroelastic material softening and dissipative nonlinearities for various piezoelectric materials; (2) combination of such material nonlinearities with standard AC-DC conversion and switching circuit nonlinearities; (3) bandwidth enhancement using a low-profile geometrically nonlinear M-shaped oscillator for primary and secondary resonance behaviors; (4) amplitude-dependent nonlinear non-conservative interacting/counteracting dynamics of material softening and geometric hardening in a broadband M-shaped energy harvester; and (5) development of a complete multi-physics electroelastic model framework accounting for material, dissipative, and 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, 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 framework is then combined with several other nonlinear effects including energy harvesting circuit nonlinearities and geometric nonlinearities exploited for bandwidth enhancement.