| Vibration is a kind of natural phenomenon widely existing in engineering including wind-induced and vehicle-induced vibration of bridges,and the aeolian vibration of transmission lines.Thanks to the vibration energy is a kind of green energy that can be used,it is of practical research significance to use the piezoelectric effect of piezoelectric materials to convert the vibration energy into electrical energy and power the sensors.The common piezoelectric vibration energy harvester is designed based on the linear or nonlinear vibration theory with a single-degree-of-freedom.There are few researches on the nonlinear piezoelectric energy harvester with a multiple-degrees-of-freedom.The nonlinear internal resonance of L-shaped structure with two-degree-of-freedom can realize wide frequency vibration.The geometric nonlinearities are introduced to establish the electromechanical-coupled distributed parameter model for a two-degree-of-freedom L-shaped piezoelectric vibration energy harvester using the extended Hamilton principle and Gauss law.The experimental research,numerical simulation and theoretical analysis are applied to investigate the broadband responses,nonlinear vibration characteristics and its applications of the energy harvester.The main research works and results are as follows:(1)The L-shaped piezoelectric vibration energy harvester based on 1:2 internal resonance principle was designed and manufactured.The nonlinear vibration experiment and output performance of the energy harvester were investigated.Two kinds of base vibration experiments were carried out on the energy harvesting system.The first one is that the output performance of the energy harvester varies with the acceleration excitation amplitude when the external resistance and the external excitation frequency are constant.The second one is the experimental investigation of forward frequency sweep.The results show that the low-frequency excitation can excite high-frequency vibration through the 1:2 internal resonance.Moreover,the voltage response generated by the high-frequency vibration is obviously larger than that of low-frequency vibration at the same excitation level,while the displacement response of the low-frequency vibration is larger than that of the high-frequency vibration.In addition,the contribution of low-frequency vibration and high-frequency vibration to voltage response increases with the increase of acceleration excitation,but the contribution of high-frequency vibration to voltage response increases more.(2)Based on the 1: 2 internal resonance principle,the electromechanical-coupled governing equations of the L-shaped piezoelectric vibration energy harvester were established and studied.The mechanism of broadening the band width and improving the efficiency of energy harvesting system were revealed.The nonlinear vibration characteristics of the energy harvesting system were verified by the base vibration experiment and the numerical simulation using ANSYS.The effect of external resistance on the damping ratio of the energy harvesting system was discussed.The effects of acceleration excitation level,external excitation frequency and external resistance on the first and second-order primary resonance response of the energy harvesting system were discussed as well.The output performance of the nonlinear internal resonance system and the linear system were compared.The results show that the experimental and numerical simulation results are in good agreement with the theoretical predictions.When the external resistance of the energy harvesting system takes the resistance corresponding to the maximum modal damping ratio,the system can harveste the maximum energy and hold the minimum vibration displacement.The performance of the nonlinear internal resonance energy harvesting system is better than that of the linear energy harvesting system.The nonlinear internal resonance energy broadens the frequency bandwidth of the resonance region under the first and secondorder primary resonance of the energy harvesting system.(3)The traditional method of multiple scales was modified and applied to investigate the nonlinear dynamic characteristics of the energy harvesting system.In the derivation of method of multiple scales,the idea of equivalent forced load was used to consider the effect of the coupling frequency appearing in the modal coordinates,and the approximate analytical solutions of the output voltage and vibration displacement of the system were derived.Some nonlinear phenomena in the output response of the energy harvester were discussed,such as jumping,nonlinear soft or hardening,quasi-periodic motion and chaotic motion,etc.The Jacobian matrix of the system was solved by the derivation results of the method of multiple scales,and the stability of the solution is judged by Lyapunov stability theory.The output response of energy harvesting system under different acceleration excitation amplitude,excitation frequency and external resistance was discussed.The results show that the results of method of multiple scales with the consideration of coupling frequency are more accurate than that of traditional one.In the forward or reverse sweep analysis of the energy harvesting system,it is found that the response will appear double jumping,which is beneficial for broadening the frequency band.Jumping phenomenon is affected by excitation frequency,external resistance and acceleration excitation amplitude.When the damping of the system is relatively small,the unstable nonlinear vibration response will appear in the internal resonance region.(4)Based on the Stockbridge type damper in aeolian vibration of transmission lines and the broad-frequency L-shaped energy harvester,a novel piezoelectric energy harvester damper with four-degrees-of-freedom was proposed.The energy harvester system was simplified into two subsystems with 1:2 internal resonance.The electromechanical coupling governing equations of each subsystem were established by Hamilton principle and Gauss law.The frequency response curves of the output voltage and vibration displacement of the piezoelectric vibration energy harvesting system were verified by experiment.According to the vortex shedding frequency of the transmission lines under the measured wind speed,an ultra-wideband piezoelectric vibration energy harvesting system that matches the aeolian vibration frequency of the lines was designed.The performance of the energy harvester to suppress the aeolian vibration of the line and to supply power for the on-line monitoring sensor was discussed.In addition,the robustness of the energy harvester under external vibration noise was analyzed by the signal-to-noise ratio.The results show that frequency response curves of the output voltage and vibration displacement are in good agreement with the experimental data.Internal resonance occurs when the external excitation frequency is close to the four natural frequencies of the energy harvester.In the internal resonance frequency range,the output power and vibration displacement of the harvester are large.The energy harvesting system can not only suppresses the aeolian vibration of the line,but also convert the aeolian vibration energy of the line into electrical energy for powering the online monitoring sensor in the wind speed range of 1-4m/s.Moreover,the energy harvesting system showed good robustness under the interference of external vibration noise.In this paper,the results of experiment,theory and numerical simulation of the L-shaped piezoelectric vibration energy harvester with 1: 2 internal resonance are beneficial to deeply understand the vibration characteristics and the energy harvesting mechanism of this harvester.Moreover,the harvester combines the idea of vibration energy harvesting and the traditional damper in transmission lines,which can effectively suppress the aeolian vibration of the transmission line and achieve online energy harvesting for sensors.This ultimately realizes the integration of power supply,sensing and vibration reduction of the line,and promotes the development of smart grids. |
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