On approximating the effective bandwidth of bi-stable energy harvesters

This paper aims to establish an analytical framework to define the effective bandwidth of bi-stable vibratory energy harvesters possessing a symmetric quartic potential 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 parameters'space are identified and used to define an effective frequency bandwidth of the harvester. The influence of three critical design parameters, namely the time constant ratio (ratio between the time constant of the harvesting circuit and the period of the mechanical system), the electromechanical coupling, and the shape of the potential function, on the effective frequency bandwidth is analyzed. It is shown that, while the time constant ratio has very little influence on the effective bandwidth of the harvester, increasing the electromechanical coupling and/or designing the potential function with deeper potential wells serve to shrink the effective bandwidth for a given level of excitation. In general, it is also observed that narrowing of the effective bandwidth is accompanied by an increase in the electric output further highlighting the competing nature of these two desired objectives.