Characterizing the effective bandwidth of tri-stable energy harvesters

Recently, it has been shown that nonlinear vibratory energy harvesters possessing a tri-stable potential function are capable of harvesting energy efficiently over a wider range of frequencies in comparison to harvesters with a double-well potential function. However, the effect of the design parameters of the harvester on the dynamic response and the effective bandwidth of such devices remains uninvestigated. To fill this void, this paper establishes an analytical approach to characterize the effective frequency bandwidth of harvesters that possess a hexic potential energy function. To achieve this goal, the method of multiple scales is utilized to construct analytical solutions describing the amplitude and stability of the intra- and inter-well dynamics of the harvester. Using these solutions, critical bifurcations in the parameter's space are identified and used to define an effective frequency bandwidth of the harvester. The influence of the electric parameters, namely, the time constant ratio (ratio between the period of the mechanical system and the time constant of the harvesting circuit) and the electromechanical coupling, on the effective frequency bandwidth is analyzed. Experimental studies performed on the harvester are presented to validate some of the theoretical findings.