Abstract

In this work, a parametric model for a frequency-up-conversion piezoelectric energy harvester (PEH) was developed based on the Galerkin method. The PEH is composed of a piezoelectric bimorph and a stopper, which was subjected to a harmonic excitation. Although backward coupling results in a structure dynamic damping, models with neglected backward coupling were often adopted to estimate the output power of a piezoelectric energy harvester. The purpose of this work is to examine the effect of backward coupling on the dynamic response and the output power generation for a frequency-up-conversion PEH. With the same base excitations, we compared the dynamics and output energies of two cases: (1) neglecting the backward coupling effect (BCE) in the model and (2) including the BCE in the model. To obtain the optimum gap with maximum output power, we studied the relationship between the output power and the gap of the steady-state solutions. From the analytical results, it was found that the BCE can be neglected as long as there is no impact or the output power is small. However, once impacts get involved, the piezoelectric backward effect dominates the total damping due to small mechanical damping which is true for most PEH. The backward coupling will significantly diminish both the vibration and output power. Therefore, if the BCE is neglected in an impact-driven frequency-up-conversion PEH, the simplified model will exaggerate the output power.

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