The Method Of Multiple Scales For Performance Analysis Of Nonlinear Piezoelectric Energy Harvester Under Parametric Excitation And Direct Excitation

Nowadays,with the rapid development of high technology,a large number of Micro-Electro-Mechanical Systems(MEMS)and Wireless Sensor Systems(WSS)have emerged.In order to provide energy for these micro devices with low energy consumption,less consumables and small volume,more and more attention has been paid.In this dissertation,a piezoelectric power generation device is based on a cantilever bimorph piezoelectric composite beam.Based on the multidirectionality and low frequency of vibration sources in real environment,as well as the complexity of damping in environment,we studied the nonlinear energy harvesting characteristics of the cantilever piezoelectric energy harvester under parametric and direct excitation.The main research work and achievements are summarized as follows:(1)Based on the assumption of Euler-Bernoulli beam,considering the geometricalnonlinearity and inextensible in the axial direction of the beam,the distributed parameter differential motion equations of the nonlinear cantilever beam piezoelectric energy harvester under parametric excitation and direct excitation are derived by using the Hamilton principle of electromechanical coupling.The Galerkin method is used to transform the nonlinear partial differential equations into the coupled ordinary differential equations.The analytical expressions of the vertical displacement amplitude,the output voltage amplitude and the output power amplitude of the piezoelectric energy harvester model are obtained by the method of multiple scales.We analyzed the effect of different excitation amplitudes,damping coefficients,load resistances on the vertical displacement amplitude,output voltage amplitude and output power amplitude of the the piezoelectric energy harvester.The results show that the linear damping coefficient and load impedance affect the initial threshold of parametric excitation.The combination of parametric excitation and direct excitation can give full play to the advantages of parametric excitation and improve the energy conversion efficiency of energy harvesting system.(2)Considering the damping nonlinearity,the differential motion equations of cantilever piezoelectric energy harvester under parametric excitation and direct excitation are extended.The analytical expressions of the vertical displacement amplitude,output voltage amplitude and output power amplitude of the piezoelectric energy harvester model are obtained by Galerkin method and the method of multiple scales.The effects of different excitation amplitudes,linear damping coefficients,nonlinear damping coefficients,resistances on the performance of the energy harvester are analyzed.The results show that the frequency response curve shows strong nonlinear hardening characteristics when the damping is small,and the nonlinear hardening effect decreases with the increase of damping.Linear damping affects the initial threshold of parametric excitation and the location of supercritical bifurcation point,while nonlinear damping does not affect the initial threshold of parametric excitation and the location of supercritical bifurcation point.(3)Based on Hamilton principle,the nonlinear motion partial differential equation of piezoelectric bimorph energy harvester model of cantilever beam with tip mass under parametric excitation and direct excitation is derived.The analytical expressions of vertical displacement amplitude,output voltage amplitude and output power amplitude of piezoelectric bimorph energy harvester system with tip mass block are obtained by Galerkin method and the method of multiple scales.The effects of excitation amplitudes,damping coefficients,resistances and tip mass on the performance of the energy harvester are analyzed.The results show that with the increase of the mass of the tip mass,the response curve of piezoelectric energy harvesting system changes from nonlinear hardening to nonlinear softening.The change of the quadratic nonlinear damping will not change the nonlinear hardening or softening characteristics of the frequency response curve.It is concluded that the introduction of the tip mass can significantly reduce the natural frequency and increase the working bandwidth of the piezoelectric energy harvester.By increasing the tip mass,the maximum output power can be obtained at the larger resistance,so that the piezoelectric energy harvester can find a better way to provide energy for the MEMS with large resistance.Adding tip mass can improve the energy harvesting effect of the model under the parameter excitation and direct excitation,and that can better play the advantages of both the parameter excitation and direct excitation.