Triple-well potential with a uniform depth: Advantageous aspects in designing a multi-stable energy harvester

Analytical expressions for the bi- and tri-stable conditions of a multi-stable energy harvester (MEH) are derived on the basis of bifurcation analyses, and the associated multi-stable regions are characterized in a 2-D parametric space. It is found that a special boundary condition exists for a triple-well with a uniform depth (T_U boundary condition), originating from a degenerate pitchfork bifurcation (DPF) point. Interestingly, the outermost well-to-well distance of the triple-well potential, when subjected to the condition that the maximum well depth is kept constant, becomes widest when the well depth is uniform. Accordingly, instead of investigating all possible parametric conditions, the design parameters for the optimal well configuration of the MEH can be sought most efficiently by simply tracing them on the T_U boundary. A detailed examination of the potential well configurations along the T_U boundary reveals that the most efficient energy harvesting from low-intensity ambient vibrations can be achieved on a T_U boundary point, near the DPF point but inevitably a certain distance apart, by inducing an enlarged interwell motion. This investigation is experimentally validated.