Energy harvesting from random vibrations of piezoelectric cantilevers and stacks
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Electromechanical modeling efforts in the research field of vibration-based energy harvesting have been mostly focused on deterministic forms of vibrational input as in the typical case of harmonic excitation at resonance. However, ambient vibrational energy often has broader frequency content than a single harmonic, and in many cases it is entirely stochastic. As compared to the literature of harvesting deterministic forms of vibrational energy, few authors presented modeling approaches for energy harvesting from broadband random vibrations. These efforts have combined the input statistical information with the single-degree-of-freedom (SDOF) dynamics of the energy harvester to express the electromechanical response characteristics. In most cases, the vibrational input is assumed to have broadband frequency content, such as white noise. White noise has a flat power spectral density (PSD) that might in fact excite higher vibration modes of an electroelastic energy harvester. In particular, cantilevered piezoelectric energy harvesters constitute such continuous electroelastic systems with more than one vibration mode. The main component of this thesis presents analytical and numerical electroelastic modeling, simulations, and experimental validations of piezoelectric energy harvesting from broadband random excitation. The modeling approach employed herein is based on distributed-parameter electroelastic formulation to ensure that the effects of higher vibration modes are included. The goal is to predict the expected value of the power output and the mean-square shunted vibration response in terms of the given PSD or time history of the random vibrational input. The analytical method is based on the PSD of random base excitation and distributed-parameter frequency response functions of the coupled voltage output and shunted vibration response. The first one of the two numerical solution methods employs the Fourier series representation of the base acceleration history in a Runge-Kutta-based ordinary differential equation solver while the second method uses an Euler-Maruyama scheme to directly solve the resulting electroelastic stochastic differential equations. The analytical and numerical simulations are compared with several experiments for a brass-reinforced PZT-5H cantilever bimorph under different random excitation levels.In addition to base-excited cantilevered configurations, energy harvesting using prismatic piezoelectric stack configurations is investigated. Electromechanical modeling and numerical simulations are given and validated through experiments for a multi-layer PZT-5H stack. After validating the electromechanical models for specific experimentally configurations and samples, various piezoelectric materials are compared theoretically for energy harvesting from random vibrations. Finally, energy harvesting from narrowband random vibrationsusing both configurations are investigated theoretically and experimentally.