Broadband modeling of a nonlinear technique for energy harvesting

This paper presents a new approach for modeling a piezoelectric harvester using a nonlinear technique under an arbitrary, including broadband and random, force excitation. Hence it extends and generalizes previous works on monochromatic force excitation to more practical and realistic applications. In the nonlinear technique, a switching device is connected in parallel with the piezoelectric element. Though its nonlinear nature together with broadband and random input suggests a numerical step-by-step analysis, this gives less insight than more analytically based methods which are difficult to conduct and have, until now, been absent. In this paper, the switching device is assumed to be turned on periodically at any chosen frequency. The concept of switching-induced self-sampling and self-aliasing is therefore introduced into the modeling. The modeling is then applied to several well-known excitation cases to validate the theory and demonstrate the effectiveness of the model. The effect of different switching frequencies when the system is subjected to a random force excitation is discussed. It is shown that the harvester gives maximum harvested power when the switching frequency is slightly less than twice the resonance of the harvester.