Enhanced energy harvesting of cantilevered flexoelectric micro-beam by proof mass

Proof mass can adjust the natural frequency of a cantilevered energy harvester to fit the vibration source frequency and, hence, improve energy efficiency. In this paper, a cantilevered energy harvesting model including a proof mass is presented based on the flexoelectric theory. The electromechanical coupling responses at steady state are obtained for harmonic excitations and then reduced to single-mode expressions for modal excitations. The flexoelectric coupling coefficient, which represents conversion of energy, is investigated. The numerical results reveal that the flexoelectric coupling coefficient can be improved by adjusting the proof mass to make the vibration frequency of the microbeam adapt to that of the ambient vibration source. The adjusting strategies have also been formulated. In addition, the flexoelectric coupling coefficient increases with the decrease in the thickness of the microbeam. As expected, the flexoelectric coupling coefficient can further be enhanced when the beam thickness reaches nanometer scale. For the beam thickness h = 0.3 μm, the current output decreases and the voltage output increases with the increase in the electrical load resistance. When the electrical load resistance is around 100 MΩ, the power output arrives at its maximum. The resonance frequency shifts from 34 693 Hz to 35 350 Hz with the increase in the load resistance from short- to open-circuit conditions, and the flexoelectric coupling coefficient for this thickness lever is kr ≈ 0.19.Proof mass can adjust the natural frequency of a cantilevered energy harvester to fit the vibration source frequency and, hence, improve energy efficiency. In this paper, a cantilevered energy harvesting model including a proof mass is presented based on the flexoelectric theory. The electromechanical coupling responses at steady state are obtained for harmonic excitations and then reduced to single-mode expressions for modal excitations. The flexoelectric coupling coefficient, which represents conversion of energy, is investigated. The numerical results reveal that the flexoelectric coupling coefficient can be improved by adjusting the proof mass to make the vibration frequency of the microbeam adapt to that of the ambient vibration source. The adjusting strategies have also been formulated. In addition, the flexoelectric coupling coefficient increases with the decrease in the thickness of the microbeam. As expected, the flexoelectric coupling coefficient can further be enhanced when the beam thickness r...