| In recent two decades,with the rapid development of micro-fabrication technology and electronic technology,the power consumption of wireless sensor systems has been declining,making it possible to use the vibration energy in the environment for powering microelectromechanical wireless sensor devices,which also promotes the research of the piezoelectric energy harvesting device.Because of its simple structure and wide response frequency band,the piecewise linear energy harvester has become the most promising research direction.Therefore,improving the theory of piecewise linear piezoelectric system is of great significance for enhancing the environmental adaptability and promoting the practical application process of energy harvester.In view of the current research status of the vibration harvesting device and piezoelectric harvesting system,the research of piecewise linear energy harvester mainly focuses on the improvement and optimization of device structure,and most analytical methods rely on experiment.However,the research on the theoretical solution of piecewise linear piezoelectric system is still insufficient.The disadvantage of the piecewise linear energy harvester is that the theoretical analysis process is complex and difficult.In this paper,the incremental harmonic balance(IHB)method is introduced to solve the problem,and relies on the method to complete the theoretical and experimental research of piecewise linear system.As a first step,A single-degree-of-freedom piecewise linear piezoelectric energy harvester is designed,and the three-dimensional model of the device is established.Based on the Euler beam theory,the equivalent parameter of mechanical structure is modeled.Considering the influence of the external load on the output performance of the system,a piezoelectric equivalent circuit model is established,and finally the dynamic differential equation of a single degree of freedom piezoelectric energy harvester is obtained.Secondly,the incremental harmonic balance method has been introduced to solve piecewise linear system.The system differential equations is calculated by incremental process and Galerkin process,and then the amplitude-frequency curve of the output opencircuit voltage of the system is obtained through numerical calculation.By comparing with the corresponding linear system,the result shows that the voltage curve of the piecewise linear system shows obvious resonance peak shift phenomenon,and the peak voltage of the system is 21.53 V and the corresponding frequency is 51 Hz.At the same time,the change tendency of output power has been analyzed with the change of the external load impedance.The maximum output power of the system is 954μW,and the corresponding external circuit load impedance value is121.43kΩ.Then,based on the stability theory,the stability of the output voltage solution of the piecewise linear system is analyzed and the amplitude-frequency curve of the stable output voltage of the system is obtained.Considering the high-voltage output performance requirements of the piecewise linear energy harvester,the external excitation conditions of the system with wide-band and high-amplitude voltage output are determined.According to the change characteristics of the system output power,the relationship between the system output power and the load impedance under different excitation frequencies is obtained,and the wide frequency bandwidth harvesting characteristics of the piecewise linear system have been analyzed by comparing with the corresponding linear system.The results show that the piecewise linear function can maintain high output power in the frequency range of nearly 5Hz,while the linear system corresponds to a frequency range of less than1 Hz.In addition,based on numerical iteration formula of incremental harmonic balance method,the influence of external excitation acceleration,the vibration mass of the main cantilever beam,the rigidity of the impact beam and the gap distance on the voltage output performance of the piecewise linear system are studied respectively.Finally,the construction of the experimental device and the experimental platform are completed,then the output voltage characteristics of piecewise linear systems and the influence of change of the key parameters on the output voltage performance of the system are experimentally analyzed,respectively.At the same time,by changing the external excitation frequency and load impedance,experimental research on the wide frequency bandwidth harvesting characteristics of the piecewise linear system is completed.The contrastive research between the experimental and theoretical results indicate that the equivalent central parameter model and the incremental harmonic balance method proposed in this paper are suitable for solving the single-degree-of-freedom piecewise linear piezoelectric energy harvesting system,and it also can provide a theoretical basis for system parameter optimization research. |
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