Research On Vibration Characteristics Of Nonlinear Piezoelectric Cantilever And Energy Harvesting

The last two decades have witnessed many advances in micro-electro-mechanical systems technologies,promoting the development of the wireless sensing,data transmission,and medical implants toward a trend of miniature and low-power.Battery,solar energy and wind energy are restricted due to its drawback,while vibration energy harvesters render a novel possible method for self-powered of low-power devices.The most common energy harvesting approach is piezoelectric cantilever beam.Traditional linear piezoelectric cantilever beam has the disadvantage of high natural frequency and narrow bandwidth,so that nonlinear piezoelectric cantilever beam energy harvesting was proposed to increase the electromechanical energy conversion and widen the bandwidth of the harvester.This paper focuses on the nonlinear dynamics of piezoelectric cantilever beam,exploring the characteristics of the nonlinear response under different random excitations.Firstly this paper a lumped parameter model is established for the nonlinear piezoelectric cantilever beam.The effects of the structural parameters on the nonlinear potential function and the nonlinear dynamic characteristics are analyzed.Since the input excitation is a key factor of the piezoelectric beam energy harvesting,and previous studies usually selected the harmonic excitation as input excitation which doesn’t conform to the aperiodic and random excitation of the real environment.Therefore,to simulate the ambient excitation more accurately,this paper generates the Gaussian white noise,band-limited white noise,the Gaussian colored noise,and the narrow-band filtered colored noise by the numerical simulation.And then take these excitations as the input excitation of the nonlinear energy harvesters to study the vibration characteristics of nonlinear piezoelectric cantilever beam.In order to analyze the probability density function of the nonlinear random response,this paper lists and simplified the corresponding FPK equation by Ito stochastic integral,and analyze the effects of harvesting circuit’s time constant ratio on the output of nonlinear energy harvester.The equivalent linearization of nonlinear system is carried out by using the method of stochastic linearization,and we discuss the equivalent linearized resonance frequency of nonlinear energy harvester for different values of the distance between the two magnets.Finally,the influence of the parameters on the nonlinear output voltage response varying with the distance between the two magnets is studied by simulation.To sum up,this paper makes a deep research on the vibration characteristics of the nonlinear piezoelectric cantilever beam.Theoretical analysis and numerical simulation reveal that properties of the noise play a important role on the efficiency of the nonlinear piezoelectric cantilever beam energy harvesting.To design a reasonable nonlinear piezoelectric energy harvester,it is crucial to check the configuration and characteristics of the noise in harvesting vibrational energy.