Research On A Kind Of Strong Nonlinear Energy Harvester Based On Complex Dynamic Frequency Method

With the development of MEMS and wireless technology,piezoelectric cantilever vibration energy harvester has attracted the attention of many researchers,and nonlinear spread spectrum technology has also been widely studied.For the energy harvester with strong nonlinearity,the traditional analytical method cannot obtain accurate results.The single degree of freedom complex dynamic frequency method is proposed to study the complex dynamic behavior of strongly nonlinear piezoelectric energy harvesters.For such systems with electromechanical coupling,there is often a half degree of freedom equation.In order to obtain more accurate approximate solutions in such systems,the single-degree of freedom complex dynamic frequency method needs to be extended.Based on the single degree of freedom complex dynamic frequency method,this paper extends and applies it to the theoretical research of multi-dimensional strong nonlinear piezoelectric energy harvester.The main contents are as follows:Firstly,based on the single degree of freedom complex dynamic frequency method,a new balance rule is introduced to make it applicable to one and a half degree of freedom system,and the approximate solution and amplitude-frequency response relationship of Duffing oscillator forced vibration are obtained.In order to further expand the application range of this method,by adding new undetermined frequency and dynamic frequency,the complex frequency method can be used to analyze the strong nonlinear vibration system with two degrees of freedom,and the approximate solution of Duffing-Van der Pol oscillator with two degrees of freedom is obtained.Comparing this method with the multi-scale method and numerical solution results,proves that the complex dynamic frequency method can study the multiple degrees of freedom strong nonlinear vibration problem.Then,considering the bending effect of the torque between permanent magnets on the piezoelectric cantilever beam,the magnetic repulsion force and torque are taken as the nonlinear boundary conditions of the free end of the oscillator.The Hamilton principle and the Galerkin truncation method are used to derive the piezoelectric cantilever beam’s distribution parameter model and the force’s boundary conditions,and the modal analysis is carried out.The magnetic force model is established by the magnetic dipole method.Under the premise of considering torque,the influence of magnetic force on the equilibrium point of the piezoelectric vibrator is observed,and the effect of torque on the piezoelectric response is quantitatively analyzed.The results show that the influence of torque on the nonlinear vibration of the harvester cannot be ignored.Finally,the complex dynamic frequency method is used to investigate how to take full advantage of the nonlinear characteristics to widen the harvester bandwidth.The complex dynamic frequency method obtains the approximate solutions of the harvester’s primary resonance and 1/3 subharmonic resonance.The energy harvesting effects of the primary resonance and the 1/3 subharmonic resonance are compared,and the generation conditions of the 1/3 subharmonic resonance are determined.The influence of the primary resonance and the 1/3 subharmonic resonance on the broadening of the frequency band of the harvester under different external excitations is analyzed.The results show that the frequency band of primary resonance can be broadened by introducing nonlinearity into the piezoelectric energy harvester,and more energy can be obtained in the global frequency range by considering 1/3 subharmonic resonance.