Harvesting Under Transient Conditions: Harvested Energy as a Proxy for Optimal Resonance Frequency Detuning

摘要

Piezoelectric-based vibration energy harvesting is of interest in a wide range of applications, and a number of harvesting schemes have been proposed and studied - primarily when operating under steady state conditions. However, energy harvesting behavior is rarely studied in systems with transient excitations. This paper will work to develop an understanding of this behavior within the context of a particular vibration reduction technique, resonance frequency detuning. Resonance frequency detuning provides a method of reducing mechanical response at structural resonances as the excitation frequency sweeps through a given range. This technique relies on switching the stiffness state of a structure at optimal times to detune its resonance frequency from that of the excitation. This paper examines how this optimal switch may be triggered in terms of the energy harvested, developing a normalized optimal switch energy that is independent of the open- and short-circuit resistances. Here the open- and short-circuit shunt resistances refer to imposed conditions that approximate the open- and short-circuit conditions, via high and low resistance shunts. These conditions are practically necessary to harvest the small amounts of power needed to switch stiffness states, as open-circuit and closed-circuit refer to infinite resistance and zero resistance, respectively, and therefore no energy passes through the harvesting circuit. The limiting stiffness states are then defined by these open- and short-circuit resistances. The optimal switch energy is studied over a range of sweep rates, damping ratios, and coupling coefficients; it is found to increase with the coupling coefficient and decrease as the sweep rate and damping ratio increase, behavior which is intuitive. Higher coupling means more energy is converted by the piezoelectric material, and therefore more energy is harvested in a given time; an increased sweep rate means resonance is reached sooner, and there will less time to harvest before the switch occurs; finally, increased damping nominally reduces the response of the system, therefore less mechanical energy is present and less energy will be harvested.