Energy Harvesting in a Duffing Oscillator with Modulated Delay Amplitude

Abstract

We study periodic and quasi-periodic (QP) vibration-based energy harvesting (EH) in a delayed Duffing harvester device in which a piezoelectric component is considered. It is supposed that the delay feedback is inherently present in the system and it is modulated with a certain frequency around a mean value. We focus attention on the case of delay parametric resonance for which the frequency of the modulation is near twice the natural frequency of the oscillator. The method of multiple scales is applied to approximate the amplitude of periodic vibrations and the corresponding power output of the harvester device. The amplitude of the QP response and the corresponding power output are determined using numerical integration. Results show that for fixed values of amplitude and frequency of the modulated delay amplitude and small values of the unmodulated delay amplitude, only periodic vibrations can be exploited to extract energy. For large values of unmodulated delay amplitude, periodic solution may turn to unstable in certain ranges of time delay and only QP vibrations can be used to extract energy with good performance.