The Nonlinear Dynamics Research Of The Bistable Piezoelectric Plate

In recent years,with the demand for the new energy,how to use piezoelectric devices for energy harvesting has been widely concerned.Vibration-based energy collection generally has the three kinds including electrostatic,electromagnetic and piezoelectric.These three types of vibration energy conversion are compared.The type of the piezoelectric can rely on the piezoelectric material itself to withstand the stress changes,and achieve the conversion of mechanical energy to electrical by the positive piezoelectric effect,so the structure of the device is usually simple.In addition to the development of piezoelectric material,it is also helpful to realize the MEMS processing of the device.Therefore,the piezoelectric transducer will have unique advantages in the miniaturization device,the integration structure and the independent self-powered occasions.In this paper,we are study the theory and experiment of the bistable piezoelectric energy harvester with simply supported by two opposite side,the other two sides are free.Firstly,the nonlinear dynamic equation of the piezoelectric plate is established,and the equation is discretized.The average equation in the polar form is obtained by using the multiple scales method.The effect of parameters on the output voltage of the system is studied by numerical simulation.Secondly,through the finite element analysis,the position of the piezoelectric film in the harvester is optimized,and the nonlinear equation of the electromechanical coupling of the optimized model is established.And the Galerkin method is employed to the first order dispersion,and the perturbation analysis is carried out by the multiple scales method and the asymptotic perturbation method.Then the influence of parameter on the system is analyzed by numerical simulation.Finally,according to the theoretical optimization model,the experimental model is established.The effect of the magnetic distance and the width of the piezoelectric material on the output voltage and the dynamics of the system are analyzed by experiments.The experimental results are compared with the theoretical results.The main contents of this paper can be divided into the following sections.(1)Based on von Karman large deformation theory,the partial differential equation for nonlinear vibration of the bistable piezoelectric system is derived by using Hamilton’s principle,and the total potential energy function of the system is obtained.Then,we usually adopt dimensionless method for the equations and the potential function of the system is analyzed.The results show that the magnetic distance has a great affect on the bistable characteristics of the system.(2)The Galerkin method is employed to discrete the partial differential equations to the ordinary differential equations.Then,the method of multiple scales is applied toperturbation analysis to obtain the nonlinear averaged equations in the polar form.The influence of the external excitation amplitude,the external excitation frequency,the piezoelectric parameter,the damping parameter,the magnetic distance and the nonlinear term on the bistable piezoelectric plate is investigated.The results show that the system shows hard spring characteristics and have multiple solutions.It is special that the effect of the nonlinear term on the system.The positive and negative values of the nonlinear term determine the characteristics of the soft or hard spring of the system.(3)The position of the piezoelectric film in the harvester is optimized by the finite element method,the nonlinear partial differential equation of electromechanical coupling of the bistable piezoelectric system is derived by the Hamilton’s principle.The Galerkin method is employed to discrete the partial differential equation,the two degrees of freedom of the electromechanical coupling equation is established.Firstly,the average equation in the polar form is obtained by using the multiple scales method.Second,the average equation in the polar form is obtained by using the asymptotic perturbation method when we considering the influence of the square nonlinearity.Finally,frequency-response curves of the piezoelectric plate are obtained by numerical simulations,and the effect of parameter on the system is analyzed.(4)Experimental study on the optimized model.The power generation of the piezoelectric energy harvester with the magnet is discussed,and the effects of the magnetic distance and the width of the piezoelectric patches on the output voltage are analyzed.The influences of the magnetic distance,the external excitation frequency and the external excitation amplitude on the nonlinear dynamic characteristics of the system are studied.