Static And Dynamic Pull-in Instability Characteristics Of Micro/nanoscale Devices

With the continuous evolution of micro/nano-electromechanical systems,the trend of equipment miniaturization greatly promotes the advancement of various electrostatically actuated devices to be utilized in the microchip,biosensor and medicine,like cells and DNA detection,and wireless communication.Therefore,the fundamental research of mechanics theories has becoming very important and urgent.Based on generalized continuum mechanics framework,this work systematically investigate the multiple physical fields coupling effect,static and dynamic pull-in instability and nonlinear dynamics behaviors of micro/nanoscale devices.The main work in the dissertation includes:(1)On the basis of the Young-Laplace equation,a size-dependent analytical model of electrostatically actuated CNTs-reinforced nanobeam is proposed in thermal environment.By utilizing the GDQ method,the equilibrium equation of CNTs-reinforced nano-actuator incorporating surface elasticity and surface residual stress is numerically solved.The influences of electrical field fringing effect,volume fraction of CNTs,temperature change and thermally corrected Casimir force and their coupling effect on static pull-in voltage and pull-in deflection are discussed.Additionally,the free-standing behavior of nano-actuator considering van der Waals force and Casimir force are compared.(2)Considering small scale effect and quantum field fluctuation,the model of CNTs-reinforced nanobeam actuator is established based on the A.Eringen’s nonlocal elasticity theory,and is numerically solved by the Shooting method with the boundary conditions of cantilever and doubly-clamped types.The influences of nonlocal parameter,van der Waals force and Casimir force on the pull-in instability of nano-actuator is studied.The analytical model of CNTs-reinforced asymmetric bilayer nano-actuator with piezoelectric layer is obtained to discuss the impacts of piezoelectric tuning voltage,nonlocal parameter,and variable width ratio of nanobeam on the pull-in voltage and pull-in deflection of nano-actuator.(3)Based on the nonlocal theory,a theoretical method is developed to investigate the static and dynamic behaviors of electrostatic FGCNTs-reinforced nano-actuator with piezoelectric layer immersed in thermal environment.The influences of the large-gap electrical force with geometrical nonlinearity,Capillary force,finite temperature and finite conductivity-corrected Casimir force on the static pull-in instability of asymmetric bilayer CNTs-reinforced nano-actuator are parametrically described.The homotopy perturbation method is employed to obtain the analytical solution between initial amplitude and oscillation frequency of nano-actuator.Moreover,the impacts of geometrical distribution of CNTs,positive/negative piezoelectric tuning voltage and temperature change on pull-in voltage and critical frequency.In addition,the transition history of systematical stability is evaluated in the phase portrait.(4)An analytical model with size dependency is proposed based on the framework of unifying nonlocal stress and strain gradient theory.The influences of nonlocal parameter,strain gradient parameter and their coupling effect on the relationship of initial amplitude and frequency are discussed in dynamic system of FGCNTs-reinforced nano-actuator.Considering the thermal fluctuation,the nonlinear dynamics characteristics of bilayered FGCNTs-reinforced nano-actuator with piezoelectric tuning are studied based on the Plasma model of thermal Casimir.The viscous damping and structural damping are incorporated to evaluate the features of time history and phase portrait of FGCNTs-reinforced nano-actuator system.(5)By employing the Gurtin-Murdoch surface elasticity and nonlocal theory,the model of electrostatically actuated circular nanoplate is presented with the consideration of surface elastic modulus and residual stress,temperature change,nonlocal parameter and process defects induced stress.The static and dynamic pull-in instability of nanoplate actuator are studied,the pull-in voltage,pull-in deflection and pull-in frequency are obtained by the analytical method.The transition procedure of pull-in instability and bifurcation of electrical circular nanoplate is described by evaluating the variation of number and position of equilibrium points in dynamic system.In addition,the influence of nonlocal parameter on the critical time history and velocity of circular nanoplate at the dynamic pull-in state is investigated.(6)Based on the nonlocal elasticity theory,the analytical model of torsional micro/nanomirror actuator with circular mainplate is proposed,and the influences of electrostatic torque,thermal Casimir torque,structural damping and squeeze-film damping on the dynamic behaviors of micro/nanomirror system are described in detail.The impact of volume fraction and geometry distribution of CNTs on the relationship of the tilting angle and pull-in voltage of torsional micro/nanomirror actuator.Considering van der Waals torque and Casimir torque,the size-dependent relation of the tilting angle and initial gap is further studied on the basis of the modified strain gradient theory.The potential energy curves and the transition of equilibrium points are used to study the procedure of stability loss of system.Furthermore,considering the coupled torsion-bending deformation of torsional nanobeam,the size-dependent analytical model of electrostatic torsion micro/nanomirror actuator with rectangular cross section is established based on modified strain gradient theory.The pull-in voltage and pull-in tilting angle obtained by couple torsion-bending model are compared to those of uncoupled torsion model,and the influence of the ratio of bending effect versus torsion effect on pull-in voltage,pull-in tilting angle and pull-in deflection are parametrically discussed.In addition,the impacted of the inner and outer geometry parameters of fixed electrodes on the pull-in instability of torsional micro/nanomirror actuator are investigated.In some special conditions,the obtained results from this work have been compared to those experiment data and other numerical results in literature,which showed good agreement.Some meaningful results and conclusion have been published in the above field.Based on the theoretical framework of the generalized continuum mechanics,this work develop the fundamental theory and analytical method on the pull-in instability characteristics and nonlinear dynamics behaviors of micro/nanoscale functional devices.Some results in this work are helpful for the application and design of MEMS/NEMS-based micro/nanoscale functional devices.