Design and Research of Triboelectric Energy Harvester for Low Frequency Nonlinear Vibration

Although great progress has been made in the study of triboelectric energy harvesting, most of the efforts are aimed at the manufacturing and experimental demonstration of the harvesters. For simultaneous energy harvesting and vibration control, there is still a strong need of structural design and in-depth theoretical research of structural dynamics of triboelectric harvesters. In this paper, a harvester in the form of a cantilever beam and two curved surfaces as constraints is proposed. When the cantilever beam vibrates under a low-frequency excitation, the contact between the cantilever beam and one of the curved surfaces is gentle and gradual. Compared with a triboelectric harvester working in the traditional contact-separation mode, this contact can achieve energy harvesting while avoiding the introduction of vibro-impact of the structure, but introduces complex nonlinear vibration. Through the planar rigid body kinematics and a quasi-static analysis, the differential equation of motion for the cantilever beam including the ninth-order geometric nonlinearity for the contact is established. The mathematical model for combining the structural dynamics and electrical dynamics is established. Finally, the approximate analytical solution of the model is obtained by using the harmonic balance method, and the stability of the model under different structural parameters is analyzed by Floquet theory. Numerical simulation results show that when the frequency excitation is 5.72 Hz, the peak output voltage is 6.9 V and the average power is 1.9 μW. When the frequency is between 5.72 Hz and 5.93 Hz, the response exhibits bifurcation. Compared with the traditional cantilever beam absorber, the frequency response curve of this structure is deflected due to the nonlinear factors brought about by the curved surface, and the frequency band of vibration hysteresis is narrow. The broadband capacity of the nonlinear spring is proven in the frequency domain for two chosen surface curvature orders, with one low and one high amplitude of excitation. Therefore, the structure proposed in this paper can maintain a larger amplitude in the broadband, thus playing a role in broadening the working frequency band of vibration absorption. In summary, the structure can not only realize vibration energy harvesting without hard impact, but also work as a vibration absorber with nonlinear characteristics.