#### Date of Award

5-2011

#### 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

Using a vibratory energy harvester (VEH) to independently power a sensor has become an increasingly popular topic due to the small amount of power current sensors require to operate. This can be achieved by scavenging energy from the ambient environment where the sensor is located. Numerous linear and nonlinear energy harvesters have been proposed in order to deal with various vibratory environments, along with improving the power production and/or bandwidth of the device.

In this thesis, we propose a technique to harvest energy from excitation sources that possess two frequency components: a fundamental component with large energy content, and a super-harmonic component with smaller energy content at twice the fundamental component. Excitations of this nature are common in the environment due to inherent nonlinearities in the dynamics of the excitation source. Normally, two separate energy harvesters are needed to extract the energy at each frequency; however, this thesis discusses a single cantilevered piezoelectric VEH that exploits the parametric amplification phenomenon to scavenge energy from both frequencies by varying the tilt angle between the axis of the beam and the direction of the excitation.

To investigate the efficacy of the proposed concept, the equations governing the electromechanical dynamics of the harvester are derived. The resulting partial differential equations and associated boundary conditions are then reduced to a single-mode Galerkin-based reduced-order model. Analytical expressions for the steady-state output power across a purely resistive load are obtained using the method of multiple scales.

Theoretical and experimental results demonstrate that parametric amplification can be used to improve the output power for given excitation parameters, beam tilt angle, and mechanical damping ratio. It is observed that there exists an optimal beam tilt angle at which the flow of energy from the environment to the electric load is maximized. This angle increases as the amplitude of the super-harmonic component of excitation increases and the mechanical damping ratio decreases. Furthermore, the resistive load of the harvesting circuit, which significantly affects the output power, is shown to have little influence on the optimal tilt angle except for very low mechanical damping ratios. Therefore, for a given environment and system parameters, an optimal tilt angle and resistive load combinations should be maintained to maximize the power output of the harvester.

Results indicate that the mechanical damping ratio plays a major role in characterizing the performance. Specifically, when the mechanical damping ratio is small, significant enhancement in the output power is attainable even when the magnitude of the super-harmonic is small as compared to the fundamental component. For instance, at a damping ratio of ζ=0.002, a 20% increase in power is observed at the optimal tilt angle when the super-harmonic component is half that of the fundamental component. However, when the mechanical damping ratio is doubled to ζ=0.004 while all other design and excitation parameters are kept constant, the enhancement of the output power drops significantly to 4%. Such findings reveal that parametric amplification can be utilized to enhance the output power of a VEH especially for micro-scale applications where the mechanical damping ratio can be easily reduced.

#### Recommended Citation

Bode, Roger, "Parametric Amplification in the Context of Vibratory Energy Harvesting" (2011). *All Theses*. 1134.

http://tigerprints.clemson.edu/all_theses/1134