Modeling and analysis of cantilever piezoelectric energy harvester with a new-type dynamic magnifier

An analytical concept of a new-type dynamic magnifier for a piezoelectric energy harvester is proposed. The new-type dynamic magnifier consists of the two-spring-mass system located between the constrained end of the piezoelectric beam and the vibrating base structure. The main function of the dynamic magnifier is capable of significantly widening the frequency bandwidth and increasing the power output from the ambient vibration. The mechanical system of the cantilever piezoelectric beam with the end mass offset and the translational and rotational springs attached to the magnifier mass offset has been modeled. The beam motions from the base (translational and rotational) and transverse relative system have been considered. A mathematical model of a cantilevered piezoelectric harvester with the new-type dynamic magnifier has been developed using the generalized Hamilton's principle. The eigenfunction and natural frequency formulations of the cantilever beam with the new-type dynamic magnifier are presented. The orthogonal conditions of the mode shapes are derived. The reduced order electromechanical coupling dynamic equations are formulated by using the present eigenfunction and the modal Galerkin decomposition method. The effect of the spring stiffness and mass offset of magnifier, and the end mass offset on the performance of the harvester is investigated. Analytical results show that with the proper selection of the design parameters of the magnifier, the harvesting power can be dramatically enhanced and the effective bandwidth of the harvester system can be improved. It is observed that a small change for the end mass offset and two-spring stiffness ratio for widening the operational frequency and magnifying the mechanical system of the piezoelectric beam may result in a substantial change of energy harvester performance.