Nonlinear performances of an autoparametric vibration-based piezoelastic energy harvester

Nonlinear characterizations of an autoparametric vibration-based energy harvester are investigated. The harvester consists of a base structure subjected to an external excitation and a cantilever beam with a tip mass. Two piezoelectric sheets bounded to both sides of the cantilever beam are used to harvest the energy. The governing equations accounting for the coupled effects of the base vibration, the response of the cantilever beam and the generated power are derived. Approximate analysis of the simplified governing equations is then performed by the method of multiple scales. The usefulness of this approach is demonstrated by deriving analytical expressions for the global frequency and damping ratio of the cantilever beam. Their dependence on the electrical load resistance is quantified. Analytical expressions for the amplitudes of the base displacement and the displacement of the tip mass are derived. An expression that relates the output power to the load resistance, global damping, and displacement of the tip mass is derived. The effects of the external force and electric load resistance on the nonlinear responses of the system are determined. The results show different responses for different operational electric loads. The broadening of the excitation regime over which energy can be harvested is analyzed. The effects of the load resistance on the types of bifurcations near resonance are determined.