Chaotification as a Means of Broadband Vibration Energy Harvesting with Piezoelectric Materials

Computing advances and component miniaturization in circuits coupled with stagnating battery technology have fueled growth in the development of high efficiency energy harvesters. Vibration-to-electricity energy harvesting techniques have been investigated extensively for use in sensors embedded in structures or in hard-to-reach locations like turbomachinery, surgical implants, and GPS animal trackers. Piezoelectric materials are commonly used in harvesters as they possess the ability to convert strain energy directly into electrical energy and can work concurrently as actuators for damping applications. The prototypical harvesting system places two piezoelectric patches on both sides of the location of maximum strain on a cantilever beam. While efficient around resonance, performance drops dramatically should the driving frequency drift away from the beam\u27s fundamental frequency. To date, researchers have worked to improve harvesting capability by modifying material properties, using alternative geometries, creating more efficient harvesting circuits, and inducing nonlinearities. These techniques have partially mitigated the resonance excitation dependence for vibration-based harvesting, but much work remains. In this dissertation, an induced nonlinearity destabilizes a central equilibrium point, resulting in a bistable potential function governing the cantilever beam system. Depending on the environment, multiple stable solutions are possible and can coexist. Typically, researchers neglect chaos and assume that with enough energy in the ambient environment, large displacement trajectories can exist uniquely. When subjected to disturbances a system can fall to coexistent lower energy solutions including aperiodic, chaotic oscillations. Treating chaotic motion as a desirable behavior of the system allows frequency content away from resonance to produce motion about a theoretically infinite number of unstable periodic orbits that can be stabilized through control. The extreme sensitivity to initial conditions exhibited by chaotic systems paired with a pole placement control strategy pioneered by Ott, Grebogi, and Yorke permits small perturbations to an accessible system parameter to alter the system response dramatically. Periodic perturbation of the system trajectories in the vicinity of isolated unstable orbit points can therefore stabilize low-energy chaotic oscillations onto larger trajectory orbits more suitable for energy harvesting. The periodic perturbation-based control method rids the need of a system model. It only requires discrete displacement, velocity, or voltage time series data of the chaotic system driven by harmonic excitation. While the analysis techniques are not fundamentally limited to harmonic excitation, this condition permits the use of standard discrete mapping techniques to isolate periodic orbits of interest. Local linear model fits characterize the orbit and admit the necessary control perturbation calculations from the time series data. This work discusses the feasibility of such a method for vibration energy harvesting, displays stable solutions under various control algorithms, and implements a hybrid bench-top experiment using MATLAB and LabVIEW FPGA. In conclusion, this work discusses the limitations for wide-scale use and addresses areas of further work; both with respect to chaotic energy harvesting and parallel advances required within the field as a whole