Analytical solutions for galloping-based piezoelectric energy harvesters with various interfacing circuits

Recently, the concept of harvesting available energy from the surrounding environment of electronic devices to implement self-powered stand-alone units has attracted a dramatic increase in interest. Many studies have been conducted on the analytical solutions of output responses for vibration-based piezoelectric energy harvesters (VPEHs), with both simple ac circuit and advanced circuits such as impedance adaptation, synchronized switching harvesting on inductor (SSHI) and synchronized charge extraction (SCE). However, very little effort has been devoted to deriving explicit output responses of aeroelastic piezoelectric energy harvesters, especially for cases involving sophisticated interface circuits. This paper proposes analytical solutions of the responses of a galloping-based piezoelectric energy harvester (GPEH). Three different interfacing circuits, including the simple ac, standard and SCE circuits, are considered in the analysis, with which the explicit expressions of power, voltage and displacement amplitude are derived. The optimal load and coupling are calculated for maximum power generation. The cut-in wind speeds for these circuits are also formulated. Wind tunnel experiments based on a prototype of a GPEH with a square sectioned bluff body and circuit simulation based on the equivalent circuit model are carried out to validate the analysis. Recommendations on the applicability of different circuits are provided based on the observed behaviors of the circuits. The proposed theoretical solutions provide significant guidelines for accurate evaluation of effectiveness of GPEHs and the scheme of normalization makes it convenient to compare devices with various parameters.