Study On Piezoelectric Energy Harvester With An Elastic Magnifier Under Parametric Excitation And Its Characteristics

As a kind of energy harvesting devices converting ambient mechanical vibration energy into electrical energy,the research on piezoelectric energy harvester has been widely attracted.It has been proved that compared with the direct resonance under direct excitation,the parametric resonance induced by parametric excitation has the potential to increase the output power up to an order of magnitude.However,it should satisfy certain conditions,that is,the amplitude of external harmonic excitation must be greater than the excitation threshold of the system.Therefore,how to reduce the excitation threshold and increase the frequency bandwidth of the system under harmonic excitation is a critical problem in the design and research of piezoelectric energy harvester subjected to parameter excitation.In addition,a similar problem occurs in the piezoelectric energy harvester subjected to random excitation,especially when Gaussian white noise is lower.To improve the performance of piezoelectric energy harvester in this circumstance,a piezoelectric energy harvester with an elastic magnifier is proposed in this thesis.The harvester is composed of an elastic magnifier mounted on the vibrating base together with a piezoelectric beam with a mass block fixed its end.Under the excitation of the vibrating base,the elastic magnifier is of direct excitation and the piezoelectric beam is of parametric excitation.This thesis also analyzed the influence of system parameters on the dynamic characteristics and energy harvesting characteristics of the harvester under both harmonic excitation and random excitation.The main work and conclusions of this thesis are as follows:1.The electromechanical coupling model of piezoelectric energy harvester with an elastic magnifier is established by using extended Hamiltonian principle.The critical value of mass block fixed the end of piezoelectric beam,which is used to decide whether piezoelectric beam is a straight beam or not,is determined,then the equilibrium points and natural frequency of the system are analyzed.For the preparation of making comparison with the harvester proposed in this thesis,the dynamic characteristics and energy harvesting characteristics of a harvester without elastic magnifier are also analyzed.2.Under a harmonic excitation,as the natural frequency of the elastic magnifier is twice that of the piezoelectric beam,the system will generate 1:2 internal resonance.The results of analysis show that the elastic magnifier performs the function of amplify very well for it reduces the excitation threshold of the system greatly and expanding the bandwidth of energy harvesting simultaneously.In addition to this,the influence of excitation amplitude,excitation frequency,structural parameters of the elastic magnifier on the dynamic characteristics and energy harvesting characteristics of the harvester are also analyzed.The results show that when the piezoelectric beam is in parametric resonance,both the elastic magnifier and the piezoelectric beam are in periodical motion with single period.Even in the case when the excitation amplitude is lower,there can generate output voltage,and the increase of excitation amplitude will lead to the increase in root mean square voltage and the energy harvesting bandwidth of the piezoelectric beam.The effects of stiffness coefficient and mass of the elastic magnifier on the excitation threshold of the harvester are similar:firstly make excitation threshold decrease then make it increase with the increase of their values.Whereas the excitation threshold will increase with the increase of damping ratio.3.For the purpose of study the performance of the harvester under a random excitation,the typical Gaussian white noise is taken as the random excitation source.The comperasion in dynamic response between the harvesters with and without elastic magnifier has been made.It can be found that when the noise intensity of excitation is lower,the former can produce obvious dynamic response but the latter can not,and when the noise intensity of excitation is higher,the dynamic response produced by the former is much stronger than that by the latter.It also can be found that with the increase of noise intensity of excitation,the root-mean-square-voltage of piezoelectric beam increases gradually,and root-mean-squaredisplacement of the elastic magnifier increases to a value then fluctuates around this value.The influence of structural parameters of the elastic magnifier on both the dynamic characteristics and energy harvesting characteristics of the harvester are studied.The results show that the optimal values for the stiffness coefficient and mass of the elastic magnifier vary with the noise intensity of excitation.With the increase of noise intensity,the optimal stiffness coefficient firstly increases and then decreases,and the optimal mass decreases;But the optimal damping ratio bears on relation to the variation of noise intensity,the smaller the damping ratio,the better the energy harvesting performance of the harvester.