On the energy extraction from large amplitude vibrations of MEMS-based piezoelectric harvesters

Abstract

As sizes decrease, the advantages of application of piezoelectric materials for mechanical to electrical energy conversion become more obvious in comparison with electromagnetic and electrostatic techniques, according to uncomplicated fabrication processes of microscale piezoelectric harvesters together with their considerable amounts of generated power. Cantilevered silicon beams with surface bounded piezoelectric layers form the main structure of these MEMS-based harvesters. Lowering the resonance frequency down to the range of environmental vibration frequencies is one of the most significant challenges in MEMS harvesters which is usually attempted to be achieved by thinning the beam and adding concentrated tip masses where both result in a sensitivity enhancement as well. Therefore, according to the amplitude and frequency of applied excitations and physical parameters of the harvester, large amplitude motions can occurr in these systems. In this study, nonlinear dynamics of a piezoelectric harvester under large amplitude vibrations is investigated. To that end first of all an accurate comprehensive fully coupled electromechanical nonlinear model is extracted through a constrained Hamilton’s variational principle. A semi-analytical approach implementing the perturbation method of multiple scales is used to solve the governing coupled nonlinear differential equations of the model and analyze the primary and superharmonic resonances. Results indicate that as excitation grows, the output power response curves are right bended leading to enhancement of the harvester bandwidth. At primary resonance a second-order harmonic of the excitation frequency is present in the output voltage as a consequence of both nonlinear curvature and inertia due to shortening effect. Furthermore, the existence of superharmonic resonances makes it possible to extract considerable amounts of power at fractions of natural frequency which is very beneficial in MEMS-based harvesters with generally high resonance frequencies.