Date of Award

8-2010

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering

Advisor

Daqaq, Mohammed F

Committee Member

Li , Gang

Committee Member

Vahidi , Ardalan

Abstract

Micro-power generators (MPGs) are compact, scalable, and low-maintenance energy harvesting devices that capture and transform wasted ambient energy into electricity.
Such devices, which are currently being researched as a possible replacement for batteries, can act as a power source to maintain and allow autonomous operations of
remote low-power consumption sensors. This thesis introduces a novel MPG which transforms wind energy into electricity via wind-induced self-excited oscillations
of piezoelectric cantilever beams. The operation concept of the device is simple: similar to music-playing harmonica that create tones via oscillations of reeds when
subjected to air blow, the proposed device uses flow-induced self-excited oscillations of a piezoelectric beam embedded within a cavity to generate electric power. When
the volumetric flow rate of air past the beam exceeds a certain threshold, the energy pumped into the structure via nonlinear pressure forces offsets the intrinsic damping
in the system setting the beam into self-sustained limit-cycle oscillations as a result of a Hopf bifurcation. The vibratory energy is then converted into electricity through
principles of piezoelectricity.
The objectives of this thesis are two folds: The first investigates the development of an analytical aero-electromechanical model to describe the response behavior of
the device, and the second deals with understanding the influence of the design parameters on its cut-on wind speed and the generated power.
To achieve the first objective, we obtain a mathematical model describing the dynamic evolution of the four essential system's parameters.
These are the spatial and temporal dynamics of the beam deflection, the temporal dynamics of the voltage developed across the electric load,
the temporal evolution of the exciting pressure on the surface of the beam, and the flow rate through the aperture between the
beam and the support. The modeling is carried out at three successive levels. First, we employ Hamilton's principle in combination with the nonlinear Euler-Bernoulli's
beam theory and the linear constitutive equations of piezoelectricity to obtain the nonlinear partial differential equation relating the flexural dynamics of the beam to
the output voltage and the exciting pressure. Second, we use basic electric circuits theories to obtain the nonlinear ordinary differential equation relating the output
voltage of the harvester to the strain rate in the piezoelectric layer. Third, assuming that the flow rate through the aperture is irrotational, two dimensional, and steady;
we utilize the steady Bernoulli's equation in conjunction with the continuity equation to relate the exciting pressure on the surface of the beam to the in- and outflow
rates of air.
Subsequently, we use a Galerkin expansion to discretize the partial differential equation into a set of nonlinearly-coupled ordinary differential equations. We carry a convergence
analysis and determine that a single-mode reduced-order mode can predict the static, linear, and nonlinear dynamic responses of the device. Additionally, we
study the influence of neglecting the beam's geometric and inertia nonlinearities on the response behavior showing that such nonlinearities can be safely ignored
within the operation range of the device. We validate the resulting reduced-order model against experimental data demonstrating good agreement for two different
configurations.
To achieve the second objective, we utilize the resulting analytical model to understand the influence of the design parameters (e.g., beam's thickness, length, chamber's
volume, aperture's width, and electric load) on the device's response with the goal of minimizing the cut-on wind speed and maximizing the output power of the
MPG. Results indicate that for a beam of a given thickness and length, there exists an optimal volume that minimizes the cut-on wind speed of the device. This
optimal volume is inversely proportional to the beam's first modal frequency. Results also indicate that the cut-on wind speed can be decreased significantly as the
aperture's width is decreased. However, it is observed that minimizing the cut-on wind speed does not always correspond to an increase in the output power. As such,
we use the resulting model to construct design charts that aid in designing a MPG with optimal design parameters for a given known average wind speed. Finally, in
an attempt to increase the output power of the device, we explore the prospect of designing the harvester such that the Hopf bifurcation responsible for the onset of
the beam's oscillation is sub-critical. Towards that end, we utilize the method of multiple scales to obtain the bifurcation's normal form, then use it to demonstrate
that the resulting bifurcation will always be super-critical.

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