| Piezoelectric energy harvester is popular due to the merits of converting vibration energy in the environment into electric energy,simple structure,high energy conversion density,easy to miniaturization and integration.However,the performance of traditional linear piezoelectric energy harvester is usually limited to a relatively narrow bandwidth.Only when the ambient excitation frequency is close to or equal to the natural frequency of the system,the system can output a large enough voltage.When the excitation frequency deviates from the natural frequency of the system,the power generation efficiency of the system will decrease sharply.It is a key problem to study piezoelectric energy harvester with wide operating band,so as to match the external environment frequency and improve the environmental adaptability of the energy harvester.This paper takes the piezoelectric energy harvester designed based on magnetic force as the research object,and studies the influence of nonlinear magnetic force on the dynamic response of the system.Two degree of freedom(2-DOF)monostable and bistable structures based on magnetic force are designed,and the power generation characteristics of the two piezoelectric energy harvesters are analyzed theoretically and experimentally.The specific work is as follows:The influence of nonlinear magnetic force on the dynamic response of the system is studied.Firstly,based on the lumped parameter model of one degree of freedom(1-DOF)nonlinear system,the dimensionless dynamic equation of the system is established.According to the characteristics of the potential function,the conditions of magnetic monostable and bistable system are determined.Then,the dynamics equations of two types of system are solved by harmonic balance method and Runge-Kutta numerical method.The broadband energy harvesting characteristics of monostable and bistable systems are analyzed respectively.The influence of different initial conditions on the electromechanical response is discussed.The results indicate that,under the influence of nonlinear magnetic force the monostable system can show nonlinear hard spring or soft spring characteristics.The amplitude-frequency curve of system output displacement bends in the direction of frequency increase or decrease,so that the system has the characteristics of broadband energy harvesting.The dynamic response of a bistable system consists of small value intrawell motion around a stable equilibrium point and large value interwell motion between two stable equilibrium points.When the system moves in intrawell motion,the output displacement amplitude-frequency curve bends in the direction of frequency decrease,showing nonlinear soft spring characteristics.When the system moves in interwell motion,the system output voltage is significantly increased and the energy harvesting bandwidth is broadened.A 2-DOF monostable piezoelectric energy harvester based on magnetic attraction is established,harmonic balance method and Runge-Kutta numerical method are applied to theoretical research to analyze its broadband energy harvesting characteristics.Firstly,the lumped parameter model of the 2-DOF monostable system is established.Based on mechanical vibration theory,piezoelectric theory and magnetic dipole model,the electromechanical coupling dynamic equation of the system is established.Then,the dynamic equation is solved by harmonic balance method in frequency-domain and the amplitude-frequency characteristic of the system output voltage expression is obtained.Meanwhile,the dynamic equation of the system is solved by numerical method in time-domain and the influence of different initial conditions on the electromechanical response of the nonlinear system is discussed.Finally,the influences of external excitation acceleration amplitude,magnet spacing and mass of auxiliary beam end on the power generation performance of the monostable system in the first two resonance regions are studied.The results indicate that,the amplitude-frequency curve of the 2-DOF monostable system output voltage exhibits linear behavior in the first resonance region and nonlinear hard spring characteristics bending in the direction of frequency increase,with coexistence of high and low energy states in the second resonance region.External excitation acceleration amplitude,magnet spacing and mass of auxiliary beam end have important effects on the frequency band width and output voltage of the system.A 2-DOF bistable piezoelectric energy harvester based on magnetic repulsion is established,harmonic balance method and Runge-Kutta numerical method are applied to theoretical research to analyze its broadband energy harvesting characteristics.Firstly,the lumped parameter model of the 2-DOF bistable system is established.Based on mechanical vibration theory,piezoelectric theory and magnetic dipole model,the electromechanical coupling dynamic equation of the system is established.Then,the dynamic equation is solved by harmonic balance method in frequency-domain and the amplitude-frequency characteristic of the system output voltage expression is obtained.Meanwhile,the dynamic equation of the system is solved by numerical method in time-domain and the influence of different initial conditions on the electromechanical response of the nonlinear system is discussed.Finally,the influences of external excitation acceleration amplitude,magnet spacing and mass of auxiliary beam end on the power generation performance of the bistable system in the first two resonance regions are studied.The results indicate that the amplitude-frequency curve of the2-DOF bistable system output voltage exists only in the first resonance region when the system moves in interwell motion.The amplitude-frequency curve of the system output voltage exhibits linear behavior in the first resonance region and nonlinear soft spring characteristics bending in the direction of frequency decrease in the second resonance region when the system moves in intrawell motion.The coexistence of high and low energy states exists when the system moves in interwell motion and in intrawell motion.External excitation acceleration amplitude,magnet spacing and mass of auxiliary beam end have important effects on the frequency band width and output voltage of the system.The experimental devices for 2-DOF magnetic monostable and bistable piezoelectric energy harvester are developed.The experimental test platform is set up.The power generation performance of two experimental devices are tested respectively.By varying the excitation frequency,the power generation performance of piezoelectric devices under different parameters is studied,and the experimental results are compared with the theoretical prediction results.The results indicate that,the experimental results of peak voltage and corresponding frequency in the first two resonance regions of 2-DOF magnetic monostable and bistable piezoelectric energy harvesters are consistent with with the theoretical prediction results.Thus,the correctness of the theoretical prediction model is fully verified.The theoretical prediction results can provide theoretical reference for the design and parameter optimization of broadband piezoelectric energy harvester. |
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