This paper developed an analytical model for a frequency-up-conversion piezoelectric energy harvester (PEH) composed of a piezoelectric bimorph and a stopper as shown in Fig.1. The whole system was subjected to a harmonic excitation. A bimodal approach was adopted to animate the beam stopper reaction. When the tip of the bimorph vibrates in free space or impacts with the stopper, a cantilever beam function was adopted. On the other hand, if the tip of the bimorph sticks with the stopper, a clamped-pinned beam function was applied to model the piezoelectric bimorph. To exam the effect of backward mechanical-electric coupling on power output, the dynamics and output energies are compared for two cases: 1) neglecting the backward mechanical-electric coupling effect in the model; 2) including the backward mechanical-electric coupling effect in the model. To obtain maximum output energy, the steady-state analytical solutions were studied to obtain the optimum gap between the piezoelectric beam and the stopper. From the results, we found that if the beam impacts and/or sticks with the stopper, the PEH model without the backward mechanical-electric coupling will exaggerate the output energy.

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