Study On Micro Inextensible Plate Piezoelectric Energy Harvester With Mass

Piezoelectric materials have both positive and negative piezoelectric effects,thus it can be applied to vibration control,piezoelectric harvester and other engineering fields.In recent years,with the development of micro-electromechanical systems(MEMS),miniaturized,integrated,portable and diverse work environment has become an inevitable trend;therefore micro-piezoelectric energy harvesters have received extensive attention from researchers.When the cantilever plates have a larger displacement under lateral load,the stresses and strains of the midplane are still very small.The nonlinearities of the inextensible plate are mainly derived from the large rotation angles.Generally,the influence of additional mass on vibration mode function is not considered when calculating the response of beam or plate system with additional mass.In this paper,the Rayleigh-Ritz method is used to study the effect of additional mass on the natural frequency and mode function of the cantilever plate.Based on the inextensible theory,the nonlinear dynamic model is established,and the influence of micro-structure,piezoelectric coupling effect and additional mass on the vibration characteristics are analyzed;the nonlinear behavior of micro-piezoelectric plates and the characteristics of the micro-piezoelectric energy harvester are also studied.The main contents of the article are divided into the following aspects:(1)The nonlinear vibration differential equation is established by using Hamilton’s principle with the application of inextensible theory,strain gradient theory and the piezoelectric effect.Based on MATLAB software,using Runge-Kutta method,the response of the micro-piezoelectric cantilever plate is obtained.The influences of the strain gradient length scale parameter and voltage on the dynamic response of micro piezoelectric cantilever plate are investigated separately.Application of the strain gradient theory increases the stiffness of the system and reduces the amplitude of the vibration.The vibration of the system can be controlled by applying an active voltage.The effect of external excitation frequency on nonlinear dynamic behavior is considered by using Poincare surface of section and diagrams of waveforms,phase and bifurcation.(2)The cantilever beam function equation with additional mass is derived;using the beam function combination method and the derived beam function equation,the structural model of the inextensible micro plate with additional mass at the cantilever end is established.The natural frequency of the micro plate is solved by the Rayleigh-Ritz method and the influence of scale effect and additional mass on vibration characteristics is studied.(3)Output voltage is an important parameter to evaluate the efficiency of piezoelectric energy harvester.Based on the cantilever plate structure,the nonlinear dynamic equation of the micro piezoelectric harvester with additional mass is established in this section;the numerical simulation is carried out by using Runge-Kutta method.The influence of the vibration mode with the change of mass on the system vibration is studied.The response of the system under different additional mass ratios is compared.Through the analysis of the output voltage,the energy harvesting effect of the micro-piezoelectric energy harvester is studied under different additional mass ratios.