Abstract
This paper presents the inverse design method for the nonlinearity in an energy harvester in order to achieve an optimum damping. A single degree-of-freedom electromechanical oscillator is considered as an energy harvester, which is subjected to a harmonic base excitation. The harvester has a limited throw due to the physical constraint of the device, which means that the amplitude of the relative displacement between the mass of the harvester and the base cannot exceed a threshold when the device is driven at resonance and beyond a particular amplitude. This physical constraint requires the damping of the harvester to be adjusted for different excitation amplitudes, such that the relative displacement is controlled and maintained below the limit. For example, the damping can be increased to reduce the amplitude of the relative displacement. For high excitation amplitudes, the optimum damping is, therefore, dependent on the amplitude of the base excitation, and can be synthesised by a nonlinear function. In this paper, a nonlinear function in the form of a bilinear is considered to represent the damping model of the device. A numerical optimisation using Matlab is carried out to fit a curve to the amplitude-dependent damping in order to determine the optimum bilinear model. The nonlinear damping is then used in the time-domain simulations and the relative displacement and the average harvested power are obtained. It is demonstrated that the proposed nonlinear damping can maintain the relative displacement of the harvester at its maximum level for a wide range of excitation, therefore providing the optimum condition for power harvesting.
Highlights
Nonlinear control can be achieved by introducing nonlinearities in the damping force or stiffness force, to enhance the performance of the system through vibration isolation [1] or energy harvesting [2]
The optimum damping is obtained in order to maintain the amplitude at its maximum level when the base excitation amplitude exceeds its threshold
For base excitation below Ymax, the shunt damping, cA, can be adjusted such that the relative displacement is at its maximum and the device operates at its optimum condition
Summary
Nonlinear control can be achieved by introducing nonlinearities in the damping force or stiffness force, to enhance the performance of the system through vibration isolation [1] or energy harvesting [2]. A nonlinear model is fitted to the optimum damping, which is dependent on the amplitude levels. The relative displacement of the harvester at resonance depends on the damping value and the base excitation amplitude. For a fixed value of cA and cI , and at a particular base excitation amplitude Ymax , the harvester can reach its maximum relative displacement. For base excitation below Ymax , the shunt damping, cA , can be adjusted such that the relative displacement is at its maximum and the device operates at its optimum condition. The average harvested power can be obtained from the shunt damping and the relative displacement as, Pave cAωn 2 Z 2. Using Eq (4) for the relative displacement, we can obtain the average harvested power in terms of the base excitation amplitude.
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