Nonlinear Dynamics of Energy Harvesting Ocean Buoys

This dissertation looks to investigate different ways that the performance of ocean energy harvesting buoys can be improved by intentionally inserting nonlinearities into the system. The goal is to maximize the amount of energy that is extracted from ocean waves across a broad range of environmental conditions. First, the bifurcation and stability behavior of inhomogeneous floating bodies is studied. Bifurcation diagrams and basins of attraction that illustrate the stability of the equilibrium positions as a function of the vertical position of the center of mass within the body are generated. Static experiments in still water are conducted to validate these results and dynamic experiments in a wave flume are carried out to examine how potential well hopping behavior can be encouraged for various wave conditions.

Next, the gimballed horizontal pendulum is studied for use as an energy harvester that can be designed for threshold escape behavior rather than the conventional method of matching frequencies. A nonlinear electromechanical model is developed to study the system's equilibrium states as a function of tilt angle. A static bifurcation point is solved for analytically and the implications for an energy harvester, one that can be designed to jump across stable attractors based on forcing amplitudes, are discussed. Amplitude sweeps are conducted showing a dynamic bifurcation point that varies as a function of frequency and effective damping and experiments are run to validate computational results.

This system is examined further to study how it can be used specifically for harvesting energy from ocean waves. Threshold escape behavior for parametrically excited systems with a time dependent term in the potential energy function is discussed and a criterion is proposed for predicting escape events. Performance metrics are identified to quantify and compare different responses. Numerical and experimental studies are conducted showing how the system can be designed for enhanced performance by altering geometric parameters to suit various excitations. The system's response to both deterministic single harmonic and stochastic multiharmonic excitations are investigated. Design implications are discussed.

Then, variable area plate capacitors are studied to determine how topological optimization can be applied to identify nonintuitive capacitor plate patterning that maximize average power dissipated through an electrical circuit during energy harvesting. Coupled electromechanical equations of motion are derived that include both the instantaneous and change in overlapping conductive area as functions of plate rotation. A genetic algorithm is used to optimize these terms and then map them to physical plate configurations. The results obtained apply specifically to the case presented, however the methods are general and can be used to solve a broad range of electrostatic energy harvesting problems.

Finally, an analytical method is developed to determine the instances in time to stroboscopically sample the response of a dynamical system subject to varying input excitations. The simplest case of a linear frequency sweep is first considered before generalizing to include more complex functions with nonlinear sweep rates and arbitrary phase shifts. This method improves the accuracy of various simulation results throughout this dissertation but can be extended to aid the analysis of any generic dynamical system.