Nonlinear Static And Dynamic Analysis Of Piezoelectric Viscoelastic Micro/Nano-beam

Microbeam and nonabeam are one of the core components inmicro-electro-mechanical systems (MEMS) and nano-electro-mechanical systems(NEMS), for instance, sensors, actuators, transistors and resonators. Their mech anicalbehavior and characterastics have been widely studied by sholars from all over theworld, and fruitfull research achievements have been obtained. Some of theachievements show that some materials used to manufacture the MEMS and NEMSshow viscoelasticity and piezoelectric effect obviously. In this dissertation, thepiezoelectric viscoelastic microbeam and nanobeam are the research object. Based onthe continuum theory, Euller-Bernoulli beam theory and piezoelectic theory, thepull-in phenomenon, adhesion, buckling, post-buckling and nonlinear dynamicstability of micro/nanobeam are analyzed considering piezeoelectric effect,viscoelasticity and external electric field. The specific contents are as follows:First of all, based on the viscoelasitic theory, Euller-Bernoulli beam theory andpiezoelectic theory, the governing equation of piezoelectric viscoelastic microbeam isformulated. Then applying Galerkin method, Leibnitz’s rule and Runge-Kutta method,the numerial results are obtained. The effects of piezoelectric voltage, DC voltage andviscoelasticity on static pull-in phenomenon under DC load are analyzed. The resultsshow that the piezoelectric voltage could control instantaneous pull-in voltage anddurable pull-in voltage of piezoelectric viscoelastic microbeam, and piezoelectricvoltage and DC voltage could adjust the collapse delay time. Under two kinds ofexternal actuated DC and AC loads, the effects of mixed voltage and piezoelectricvoltage on the dynamic pull-in phenomenon are analyzed, too.Secondly, based on the thermodynamics theory and introducing the peel numberand corresponding physical meaning, the effects of piezoelectric effect and geometricparameters on the peel number of the microbeam under adhesion state are analyzed. Itis got that peel number increases with the raise of piezoelectric voltage whichprovides theoretical possibility of repairing the microbeam under adhesion state. Thegeometric parameters also affect the peel number apparently, which causes certainrestrictions on the design of MEMS and NEMS.Thirdly, based on the continuum theory and Euller-Bernoulli beam theory, thestatic governing equation and the certain solution conditions of piezoelectric viscoelastic nanobeam are obtained considering the action of van der Waals forcebetween the nanobeam and baseplates. Through Galerkin method and quasi elasticmethod, the buckling and post-buckling behavior of piezoelectric viscoelasticnanobeam is analyzed.Finally, applying incremental harmonic balanced method, the nonlinear dynamicstability of a piezoelectric viscoelastic nanobeam under a periodic piezoelectricvoltage is studied. In the numerical calculation, the effects of piezoelectric effect,viscoelasticity and van der waals forces on the principal region of instability arediscussed.