Development and applicability of low-fidelity solutions for electret-based microcantilever energy harvesters

An electrostatic energy harvester is investigated where the reduced-order model is developed accounting for the electrical and mechanical nonlinearities. To overcome the difficulty of dealing with such a nonlinear model, an analytical approach based on the method of multiple scales is employed to create analytical solutions for displacement, electrical charge, and power of this harvester. The reduced-order model with the analytical solutions makes this approach novel and unique. The limits of applicability of this approach is determined by comparing the analytical solutions with solutions obtained using numerical integration. The results show that with estimating the effective nonlinearity as suggested in this approach, it is possible to interpret the behavior of harvester for a variety of operating conditions. The effective nonlinearity decreases more for a particular electrical load resistance as the electret voltage increases. However, the effective nonlinearity increases for a particular electret voltage as the electrical load resistance increases. When effective nonlinearity becomes very small, the behavior of the harvester turns into almost linear, and the matching of solutions of method of multiple scales with solutions of numerical integration is perfect. But, when the effective nonlinearity is significant, the deviation between solutions of method of multiple scales and solutions of numerical integration becomes noticeable. Moreover, increasing acceleration amplitude of the base excitation for cases of significant effective nonlinearity creates a bounded motion with softening behavior.