Date of Award

December 2016

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

Committee Member

Mohammed F Daqaq

Committee Member

Ardalan Vahidi

Committee Member

Gang Li

Committee Member

Lonny L. Thompson


When a container carrying a magnetized ferrofluid is subjected to external mechanical stimuli, the sloshing motion of the magnetized ferrofluid generates a time-varying magnetic flux, which can be used to induce an electromotive force in a coil placed adjacent to the container. This process generates an electric current in the coil, and therewith, can be used to transduce external vibrations into electric energy providing a unique approach for vibration energy harvesting using liquid-state transduction materials. As compared to traditional vibratory energy harvesters that employ soli transduction elements, this approach offers several advantages including, but not limited to, conformability to different shapes and increased sensitivity to external excitations. In this dissertation, a bench-top experiment was first constructed to demonstrate the feasibility of the proposed concept for vibratory energy harvesting. A rectangular plastic container carrying ferrofluid was placed inside a pick-up coil which is wound around a ferrite core. The whole setup was mounted on an electrodynamic shaker table which provided a controlled acceleration at the containers base. The external magnetization is applied using permanent magnets with maximum magnetic field intensity of 92 mT. Series of experiments were carried out to determine the optimal configuration of coil windings with respect to the sloshing and magnetic field directions. It was found that the output power of the device increases an order of magnitude when the coil is wound perpendicular to the sloshing motion and magnetic field lines. For the optimal configuration determined experimentally, a nonlinear analytical model which governs the electro-magneto-hydrodynamics of the harvester was developed. An approximate analytical solution of the model was obtained using perturbation methods for two different types of excitation; namely for a case involving the primary resonance excitation of the first mode and a case involving the principle parametric resonance of the first two modes. For the case involving the primary resonance of the first mode, it was observed the approximate analytical solution fails to capture the qualitative behavior of the harvester’s response for some ferrofluid height to container width ratios. Upon further inspection, it was observed that for those critical height-to-width ratios, the sloshing conditions are such that a two-to-one internal resonance between the first two sloshing modes can be activated. To account for the internal resonance, a modified version of the perturbation solution was devised and used to obtain a solution of the governing equations capable of capturing the influence of the internal resonance on the dynamics. Overall, it was shown that the developed model is capable of capturing the qualitative behavior of the dynamics of the harvester for both cases of excitation and for various magnetic field distributions. It was observed that the orthogonality of the magnetic field distribution along the width the container to the shape of the mode being excited plays a critical role in determining the output power of the harvester. Specifically, regardless of the input excitation level and the size of the induced sloshing waves, very little energy can be harnessed from the environment when the magnetic field distribution is an even (odd) function of the containers width while the mode shape being excited is an odd (even) function of the width. It was shown that, unlike the primary resonance scenario, a threshold excitation level must be achieved in the principle parametric resonance case before the harvester can produce measurable voltage levels. This threshold increases with the strength of the applied magnetic field.