Nonlinear analysis of micro piezoelectric energy harvesters

This article proposes a framework for determining the types of nonlinearity observed in the frequency response of microscale energy harvesters made of a piezoelectric film deposited on a stainless-steel substrate. The model accounts for inertial, geometrical and material nonlinearities due to amplified excitation and induced hysteresis. The simulations based on the multiple scale analysis reveals the softening type of nonlinearity for the case of a 15 μm PZT thick film deposited on a 60 μm stainless-steel substrate. They agree quite well with the experimental observations. In addition, the further investigation shows the existence of the critical film thickness such that the hardening (softening) nonlinearity is observed if the film thickness is below (above) this critical value. It is also found that such a key parameter is mainly affected by the ratio of the bending stiffness due to material nonlinearity to that based on linear moduli. Finally, the hardening type of nonlinearity was also observed in different samples with very small film thickness, as predicted by the proposed framework.