Effect of piezoelectric material nonlinearity on vibration-based piezoelectric energy harvesting

Vibration-based piezoelectric energy harvester (VPEH) has received significant interests in the last couple of decades. In recent years, more emphasis has been given to the understanding and modeling the effect of nonlinearities introduced by mechanical and electrical aspects of the system, while the nonlinearity induced by the piezoelectric material is usually ignored. However, it has been experimentally found that this material nonlinearity can have a significant effect on the system behavior even at low to moderate excitation level. This paper is motivated to consider this piezoelectric nonlinearity in the system model, and study how the nonlinearity affects the power characteristics of the system, most importantly, the power limit and electromechanical coupling. Through a harmonic balance analysis, an approximated model is developed from a nonlinear model proposed in the literature, and allows for deriving closed-form expressions of important power characteristics. The approximated model elucidates the effect of piezoelectric material nonlinearity, which is represented by a nonlinear damping term and a nonlinear stiffness term. It is revealed that the addition of piezoelectric material nonlinearity results in interesting power behaviors that are largely different from that of a VPEH without piezoelectric nonlinearity. For instance, the power limit is reduced by the nonlinear damping induced by the piezoelectric nonlinearity. In addition, the critical electrical coupling, also known as the minimum electromechanical coupling for the system to possible reach the power limit, increases with the base excitation. A strongly coupled VPEH with piezoelectric nonlinearity under low excitation could become weakly coupled under large excitation.