New insights into piezoelectric energy harvesting using a dynamic magnifier

This manuscript considers the design and performance of a piezoelectric vibration-based energy harvester with a dynamic magnifier (VEHDM) to a traditional single degree-of-freedom harvester (VEHS) using proper metrics. Past research has shown that the addition of the second magnifying mass can increase the peak power harvested by as much as 20 times [1] when compared to the VEHS; however, the metrics of performance comparison were not clearly defined, nor was the comparison carried at optimal loading conditions. For instance, the peak power was compared at different excitation frequencies and power not power per unit mass is used for comparison purposes. Additionally, the VEHDM is designed so that the magnifier mass and stiffness are considered independent of the primary stiffness and mass of the harvester. In this study, we determine the optimal properties of the magnifier, in terms of frequency ratios and resistance that maximizes both power and power density for a fixed frequency harmonic excitation. The optimized VEHDM is compared to a similarly optimized VEHS. Treating the magnifier as a tuned mass damper (TMD), i.e., simply adding the magnifying mass and stiffness to the optimized VEHS and then tuning the magnifier to split the resonance peak of the single mass harvester, increases the peak power harvested for mass ratios greater than one. However, the peak frequencies of excitation of the VEHS and VEHDM differ. Only at large values of the mass ratio does the excitation frequency of the VEHS and VEDHM coincide, making the VEHDM less efficient in terms of power per unit mass. Similarly, simply adding a magnifying stiffness and mass to the optimized VEHS and then tuning both the VEDHM to the VEHS's to the same excitation frequency by changing the the uncoupled natural frequency of VEHDM's magnifier components limits the performance of the VEDHM. In this case, the VEHDM generates the same amount of power as the VEHS. Nonetheless, the VEHS is more efficient in terms of power generated per unit mass. In order to match the single mass harvester's power per unit mass, the optimal magnifier for the VEHDM is a rigid spring of negligible mass acting in series with the stiffness with the VEHDM's piezoceramic element. However, significant gains in both peak power and peak power per unit mass for a fixed frequency excitation can be obtained by considering all the mass and stiffness elements in the VEHDM, while using the same piezoelectric in the VEHS.