Theoretical And Finite Element Simulation Research On Piezoelectric Energy Harvester Of Cantilever Beam With Variable Stiffness

With the wide application of wireless sensors and some portable electronic devices,how to power these low-power microelectronic devices has become a hot issue in current research.Piezoelectric energy harvester is a device that captures vibration energy from the environment by using a piezoelectric conversion structure based on the positive piezoelectric effect.It has the advantages of high energy density,no pollution,simple structure and easy integration,and can supply energy for microelectronic devices.The research of piezoelectric energy harvester is one of the hot trends in the research of mechanical vibration,and how to realize the low-frequency energy harvesting of piezoelectric energy harvester,improve its output power and broaden its vibration frequency band is the core issue of current research.In this paper,several kinds of cantilever beam with variable stiffness piezoelectric energy harvesters are studied via theoretical and finite element simulation.Firstly,aiming at realizing the low-frequency energy harvesting and improving the output power of piezoelectric energy harvester,a cantilever beam piezoelectric energy harvester with two steps of different thicknesses is proposed and studied.Then,two methods are used to broaden the vibration frequency band of the energy harvester.One is to introduce nonlinear magnetic potential energy into it,and a cantilever beam piezoelectric energy harvester with stepped variable thicknesses and permanent magnetics is investigated.The other is that the two-stepped structure is extended to the periodic-stepped structure,and a cantilever stepped beam with periodically variable thicknesses piezoelectric energy harvester is examined.Finally,an axially functionally graded cantilever beam piezoelectric energy harvester is explored.The research content of the thesis mainly includes the following aspects:(1)Study on theoretical modeling and energy harvesting characteristic of a cantilever beam with two steps of different thicknesses piezoelectric energy harvester.The coupled electromechanical governing equations for the piezoelectric energy harvester are established by means of the Lagrange equations,and expressions for the steady-state response are obtained.The output voltage,harvested power and power density frequency response curves for different geometric parameters and load resistances are obtained by numerical analysis.The finite element simulation is used to verify the validity of the theoretical model,and the effects of geometric parameters on the natural frequency,output voltage,harvested power and power density of the energy harvester are fully studied.The performance between the proposed cantilever beam with two steps of different thicknesses and the conventional uniform cantilever beam piezoelectric energy harvester is compared.(2)Theoretical modeling and response analysis of a cantilever beam with stepped variable thicknesses and permanent magnetics piezoelectric energy harvester.A pair of permanent magnets is added on the basis of a cantilever beam with stepped variable thicknesses piezoelectric energy harvester,and introducing nonlinear magnetic potential energy,the coupled electromechanical governing equations of the system are derived via the Lagrange equations.The fourth-order Runge-Kutta method is utilized to simulate the governing equations of the system,and the influence of the distance between two magnets on the characteristics of the system is examined.Moreover,the mono-stable and bi-stable responses are analyzed,and the effects of the distance between two magnets and external excitation amplitude on the vibration and voltage responses are investigated.(3)Study on vibration and energy harvesting characteristics of a cantilever stepped beam with periodically variable thicknesses piezoelectric energy harvester.The transfer matrix method is employed to calculate the natural frequencies of the finite periodic piezoelectric cantilever beam with stepped variable thicknesses and the band structure of corresponding infinite periodic beam,and the influence of geometric parameters on the natural frequency and the first band gap of the beam are investigated in detail.The correctness of the calculated band gap results by the transfer matrix method is verified via the finite element simulation.In addition,the vibration and voltage responses of the finite periodic piezoelectric cantilever beam with stepped variable thicknesses in the first band gap are explored using the finite element simulation,and the performance between the cantilever stepped beam with periodically variable thicknesses and the conventional uniform cantilever beam piezoelectric energy harvester is compared.(4)Study on vibration and energy harvesting characteristics of an axially functionally graded cantilever beam piezoelectric energy harvester.The shape of the beam is considered as rectangular,trapezoidal and triangular.To begin with,the free vibration of the system is studied by using the asymptotic development method,and the approximate analytic expression of the natural frequency is derived.Furthermore,a finite segment model is proposed,the finite element simulation is utilized to verify the accuracy of the results calculated by the asymptotic development method,and the effects of gradient parameter and geometric parameter on the fundamental frequency are explored.Ultimately,the finite element simulation is employed to study the energy harvesting characteristic of the system,and the influences of gradient parameter and geometric parameter on the voltage frequency response curve are analyzed.