Energy harvesting under excitations of time-varying frequency

The design and optimization of energy harvesters capable of scavenging energy efficiently from realistic environments require a deep understanding of their transduction under non-stationary and random excitations. Otherwise, their small energy outputs can be further decreased lowering their efficiency and rendering many critical and possibly life saving technologies inefficient. As a first step towards this critical understanding, this effort investigates the response of energy harvesters to harmonic excitations of time-varying frequency. Such excitations can be used to represent the behavior of realistic vibratory environments whose frequency varies or drifts with time. Specifically, we consider a piezoelectric stack-type harvester subjected to a harmonic excitation of constant amplitude and a sinusoidally varying frequency. We analyze the response of the harvester in the fixed-frequency scenario then use the Jacobi-Anger's expansion to analyze the response in the time-varying case. We obtain analytical expressions for the harvester's response, output voltage, and power. In-depth analysis of the attained results reveals that the solution to the more complex time-varying frequency can be understood through a process which "samples" the fixed-frequency response curve at a discrete and fixed frequency interval then multiplies the response by proper weights. Extensive discussions addressing the effect of the excitation parameters on the output power is presented leading to some initial suggestions pertinent to the harvester's design and optimization in the sinusoidally varying frequency case.