On electrical optimisation using a Duffing-type vibrational energy harvester

There has been much recent interest in the response analysis and optimisation of the linear energy harvester under ambient vibrations. To transfer maximum power to an electrical load in a resonant system, the load resistance should be equal to the sum of the electrical analogue of mechanical damping and internal resistance. However, principally because of the limited bandwidth offered by the linear energy harvester, the potential benefit of nonlinearity has recently been applied to improve the effectiveness of energy harvesting devices. For example, a Duffing-type oscillator can provide a wider bandwidth and greater effectiveness when subject to periodic excitations. The motivating hypothesis has been that the nonlinear Duffing energy harvester can also be optimised to maximise the available electrical power. This paper presents theoretical optimisation and numerical studies under three different conditions with the designed Duffing-type devices. First, the simplest model without any transmission mechanism and optimisation constraints is considered. Second, a device operated under low frequency and large force excitations using a ball screw to convert low-speed linear motion to high-speed rotation is analysed, where the optimum lead and load resistance are derived. Finally, considering the limitation of some dimensions in practical implementation, the constrained optimisation subjected to the maximum displacement of the seismic mass is also shown in this paper.