Size effect of tip mass on performance of cantilevered piezoelectric energy harvester with a dynamic magnifier

A distributed-parameter model of cantilevered piezoelectric beam with a dynamic magnifier has been proposed for the efficient analysis of a piezoelectric energy harvester, but there appears no beam model suitable for a piezoelectric energy harvester with tip mass offset and a dynamic magnifier. To deal with tip mass offset, the size effect of tip mass offset on the kinetic equation and boundary condition has been considered. A modified model of cantilevered piezoelectric energy harvester with tip mass offset and a dynamic magnifier has been developed by using the generalized Hamilton's principle. Analytical formulation of the eigenfunction and natural frequency of the modified model have been presented. The modified model has been demonstrated by parametric studies. The results obtained show that the harvesting power can be dramatically enhanced with proper selection of the design parameters of the dynamic magnifier and tip mass offset. The tip mass offset significantly affects the accuracy of the analysis. It is observed that even a small change in tip mass geometry results in a substantial change of energy harvester performance, not only to change the resonant frequency but also to affect the strain distribution along the energy harvester length. The modified model is more suitable for the harvester with tip mass offset and dynamic magnifier.