Electromechanical modeling of macro-fiber composite piezoelectric and pendulum-based electromagnetic devices

This dissertation investigates electromechanical modeling of Macro-Fiber Composite piezoelectric material-based devices and pendulum-based electromagnetic energy harvesting systems. Both devices have many applications in vibration-based energy harvesting, besides having other uses as sensors and actuators.The Second Chapter investigates vibration energy harvesting from a beam with unconventional boundary conditions. The beam in consideration has multi-point constraints. It is shown that the natural frequencies, strain uniformity along the beam, and strain node positions can be adjusted by shifting the support locations. The Third Chapter presents a new continuous electric field model for the Macro-Fiber Composite device for both energy harvesting and actuation applications. The differential form of Gauss’s law is used to obtain spatial terms of the electric field, and the integral form of Gauss’s law is used to obtain temporal term of the electric field. The matched asymptotic expansion method is employed to obtain the electric field between two pairs of interdigitated electrodes under quasi-electrostatic conditions. Generalized Hamilton’s principle is employed to obtain the coupled electromechanical equations of motion for a beam with the Macro-Fiber Composite device. The Euler-Bernoulli assumptions are used to approximate strain distribution. Under current assumptions, equivalent capacitance and electromechanical coupling terms are obtained without using discontinuous functions (e.g., Heaviside or piecewise functions) for electric field terms. The equivalent capacitance is within 2% of the values reported by the manufacturer. Frequency response functions are obtained for the energy harvester and the actuator by assumed modes solution for a cantilever beam. It is shown that the actuator's current is related to the optimum working load of the energy harvester by Ohm’s law. The Fourth Chapter investigates oscillatory and rotary response of pendulum-based electromagnetic generators under an open circuit condition for two different models considering the lower arm’s rotational motion during walking. An arm pitching model is utilized to represent the swing of the lower arm during walking. An arm rolling rotation model is used to represent the twisting type motion of the lower arm movement, for example, from tremors experienced by Parkinson’s patients. The governing equations of motion around the stable equilibria are derived using Lagrange formulation, and their non-dimensional forms are introduced. The generator parameters used in the parametric analysis are identified by fitting frequency response functions on the experimental data. The system’s dynamics shows various bifurcations, including limit point bifurcation, pitchfork bifurcation, a cascade of period-doubling bifurcations under amplitude or frequency sweeps. The Fifth Chapter examines energy harvesting from the pendulum-based electromagnetic generator when placed on the different human body joints. By substituting the in-plane trajectories of joints (wrist and elbow) from a body motion simulation software into the coupled electromechanical equations of motion of the electromagnetic generator, energy harvesting from the electromagnetic generator is investigated under the normal walking motion. It is shown that the system’s response is always an oscillatory type with the same period of walking motion, and the output power can be maximized by varying the external load resistance at each specific relative walking velocity. Moreover, the higher walking velocity results in a higher output power from the generator. Ph.D.Includes bibliographical reference