Study On The Steady-state Response Of A Piezoelectric Cantilever Beam Under Base Noise Excitatio

Vibration-based energy harvesting has become the main research field of micro-power generation devices.Piezoelectric transducers have received attention from many scholars because of their ability to convert the mechanical energy of vibration in the ambient into electrical energy.The cantilever beam piezoelectric energy harvester is a simple structure,has lower processing difficulty,and is widely used.Because the linear piezoelectric cantilever beam has a narrow frequency bandwidth,it can only operate effectively when the excitation frequency is close to the fundamental frequency.The nonlinear terms in the model are helpful to broaden the stimulated frequency bandwidth,therefore,the key issues of this topic are add nonlinear terms to the model to appropriately,then to use stochastic nonlinear dynamics theory on the response of the piezoelectric cantilever under the excitation of the base noise,and to explore the output characteristics of the piezoelectric cantilever under different excitations.The main work of this paper is:(1)The Lagrange equation is used to model and dimensionless the piezoelectric cantilever beam under random signal excitation.The basic noises considered in this study are Gaussian white noise and Gaussian colored noise.Then the dynamic equation and the piezoelectric equation are transformed into two stochastic differential equations about the transient equivalent amplitude and the transient phase,and then the stochastic differential equation is simplified into an Ito type equation about the equivalent amplitude by using the principle of stochastic averaging.Drift coefficient and diffusion coefficient are obtained.On this basis,when the noise intensity and time delay coefficient are taken as different values,the steady-state probability density function(PDF)of beam displacement and transient output voltage,the joint PDF of displacement and velocity are obtained.(2)Aiming at the dimensionless model of Duffing piezoelectric energy harvester under Gaussian white noise excitation,an improved random average method is proposed.Using a simplified method based on the idea of energy balance method,an approximate expression of frequency ω(A)is directly obtained,and then a strong nonlinear random averaging method is used for simplification.After obtaining the drift coefficient and the diffusion coefficient in the Ito equation,the response displacement,steady-state probability density of response voltage,joint probability density of velocity displacement,mean square response of voltage and other key values are all obtained.The influence of each system parameter on the mean square value of output voltage is studied.The results are compared with the Monte Carlo numerical simulation results.(3)The improved strong nonlinear random average method is used to theoretically analyze and solve the steady-state response of the piezoelectric cantilever beam model under Gaussian colored noise excitation.The response amplitude of the system and the steady-state probability density of voltage are obtained.The joint probability density of displacement and velocity,the mean square value of voltage and other key values,are analyzed to investigate of the noise intensity,damping coefficient,nonlinear stiffness coefficient and time delay coefficient on the system response,and finally passed numerical simulation verifies the validity of the theoretical method.