Nonlinear Modeling And Study Of Piezoelectric Energy Harvester With Additional Mass Frame

Piezoelectric energy harvester can convert the energy generated by vibration into electricity,and then supply power to other electronic devices and it has become a hot issue for scholars in recent years.Piezoelectric energy harvester is usually simplified as a cantilever structure and its working frequency band is in the resonant region where large deflection and large rotation usually occur.Therefore,the study of cantilever structure under large deflection and large rotation angle is the theoretical basis for the study of piezoelectric energy harvester.The output voltage is an important index to measure the quality of the piezoelectric energy harvester.It is an effective way to increase the output voltage by widening the effective working frequency band of the piezoelectric energy harvester.The main research contents of this article are as follows:(1)The coordinate transformation,nonlinear strains and curvatures were considered for flexible cantilever plates with large deflection and rotation angle.The nonlinear partial differential equations and boundary conditions of cantilever plates were established by Hamilton’s principle.The stress functions related to the internal forces and shear forces in the middle plane were deduced,and the expressions of the deflection and stress functions were given.The relationship between the stress and deflection functions was given using the principle of minimum potential energy.Applied to Galerkin method,the system of nonlinear ordinary differential equations were obtained.(2)Under the condition of uniform load,the questions of the static bending and vibration for flexible cantilever plates were studied by theory and static experiments.The load-deflection curves of plates under different theories were investigated,and the effects of nonlinear strains and curvatures on the static bending deformation of the plates were analyzed.The harmonic balance method was used to analyze the nonlinear amplitude-frequency response,and the nonlinear characteristics of the system were summarized.The Longo-Kutta method was used to investigate complex nonlinear behaviors such as bifurcation and chaos.(3)A novel combined structure with additional mass frame was designed by combining rigid body vibration of mass frame and bending vibration of cantilever plate.which can reduce the natural frequencies and widen the working frequency band.The first three modes and natural frequencies of the piezoelectric energy harvester were investigated by finite element method to verify the feasibility of the idea.According to the modes obtained by finite element method,the theoretical expression of mode functions was derived,and the natural frequencies of the system were solved by Rayleigh method and compared with the results of finite element method,which laid the theoretical foundation for the analysis of piezoelectric energy harveater in the future.(4)The new structure proposed above was applied to the piezoelectric energy harvester.Based on the theory of nonlinear plate theory and Hamilton’s principle,the nonlinear dynamic equations of the piezoelectric energy harvester with additional annular mass frame was established.The vibration and electric power generation characteristics of the piezoelectric energy harvester were investigated,and the influence of structural parameters on the energy capture efficiency was analyzed.