Theoreticaland Numerical Analysis Of Bi-stable Piezoelectric Energy Harvesting System With Elastic Support

The wide application of wireless sensors and mobile electronic devices have greatly promoted the development of vibration energy harvesting technology.This long-term energy harvesting technology has broad application prospects and huge potential commercial value in military equipment,field monitoring and intelligence.Therefore,it has naturally became a hot topic and frontier research for scholars in the field of vibration in China and abroad to fully use the potential value of the design and improve the energy conversion efficiency.In this paper,the dynamic behavior of a piezoelectric cantilever energy harvesting system with bi-stable state under elastic support is studied.Based on the magnetic force model which can induce bi-stable phenomena,the mathematical model of the system with two degree of freedom under harmonic base motion is firstly established using Newton’s second law and Kirchhoff’s law.By the Routh-Hurwitz criterion,the static bifurcation of equilibrium point is secondly analyzed after reducing the dimensionless governing equations as state equations with five dimension,and the bi-stable phenomenon is explained by the nonlinear potential function analysis.In addition,the variation of how the displacement and the output voltage of the piezoelectric cantilever beam changes with the system parameters and excitation parameters are obtained by using Matlab numerical simulation,and the distribution of the displacement and output voltage of the piezoelectric cantilever beam with respect to the system parameters and excitation parameters is obtained based on the Poincaré mapping.The averaging equation of the bi-stable piezoelectric energy harvesting system is derived by the method of multiple scales,and the amplitude-frequency characteristic equation of the system is given according to the existence condition of the average equation.Based on the amplitude-frequency characteristic equation,the system parameters and external excitation parameters are analyzed by homotopy continuation method.At the same time,the three-dimensional diagram is made under different parameter combinations based on the amplitude-frequency characteristic equation.1.Both the numerical and analytical results show that the amplitude-frequency curves of the system are in hard characteristic.However the variation of the amplitude of piezoelectric cantilever beam with mass and stiffness ratio are in soft characteristic.From time histories and phase trajectories,the harmonic response of the system may bifurcate,which can lead to complex periodic motion or quasi-periodic motion,even chaotic motion when the parameters of the system are changed.The motion of the system can take place near the zero or non-zero equilibrium point,even jump with large amplitude between the two non-zero equilibrium points.2.What ’ s more,under the same parameters,the system has more significant nonlinear characteristics in the bi-stable compared with mono-stable state,and the application of bi-stable system significantly improved the voltage output and response frequency band of the system,and compared with the linear system,results show that the introduction of nonlinear magnetic force significantly increases the voltage output of the system.3.The results of the three-dimensional graph analysis show that when considering the internal resonance,the amplitude of the piezoelectric cantilever beam is larger than that of the bi-stable state when the system is mono-stable,and the amplitude of the piezoelectric cantilever beam varies with different system parameters and external excitation parameters.The change provides theoretical guidance for the design of the energy harvester,that is,whether the system at in mono-stable state or bi-stable state,the lower mass ratio and higher stiffness ratio should be selected for parameter combination.The results of the numerical analysis agree well with the approximate results obtained by the the method of multiple scales.