Analysis For The Influence Of Surface Effect On Mechanical And Electromechanical Behaviors Of Nano-scale Beams And Plates

Due to their superior mechanical, electronical and thermal properties, nanomaterials have been widely used in mirco- or nano-electromechanical systems(MEMS/NEMS) such as sensors, switches and actuators. As their sizes reduce to nanoscale, the surface-to-bulk ratios of nanostructures rapidly increase. In this situation, surface energy could significantly affect the mechanical behaviors of nanostructures. Therefore, it is essential to understand the effect of surface energy on the mechanical responses of nanomatericals. In this thesis, the influence of surface effect on beam-like and plate-like nanostructures is investigated. The main research contents and conclusions are listed as follows:The effects of surface and interface energies on the bending behavior of nanoscale multilayered beams are investigated. Through the principle of minimum potential energy, the governing equations and boundary conditions are derived. The closed-form solutions are presented and the overall Young’s modulus of the beam is studied. The surface and interface energies are found to have a major influence on the bending behavior and the overall Young’s modulus of the beam. The effects of surface and interface energies on the overall Young’s modulus depend on the values of the surface/interface elasticity constants and the initial surface/interface energy of the system. The results can be used to guide the determination of the surface/interface elasticity properties and the initial surface/interface energies of the nanoscale multilayered materials through nanoscale beam bending experiments.Based on Timoshenko beam theory, the effect of surface energy and attached mass on the vibration of nanotube is studied. The governing equation is derived by using Hamilton principal and solved numerically.The results show that the traditional model, which neglects the surface energy, predicts a higher attached mass and lower sensitivity of the sensor. On the other hand, neglecting the transverse shear deformation and rotary inertia of the sensor will result in a lower prediction of attached mass and a higher prediction of sensitivity of the sensor.The influence of the surface and small-scale effects on the bending and electromechanical coupling behavior of a piezoelectric nanobeam is studied by using the beam bending model. Explicit formula for electromechanical coupling(EMC) coefficient of the piezoelectric nanobeam is obtained. It is found that the effect of surface stress on EMC coefficient of the piezoelectric nanobeam is more significant for a slender nanobeam. The effect of nonlocal elasticity on the EMC coefficient increases with increasing the nonlocal parameter. In addition, the influence of surface effect on the bending and energy generating performance of piezoelectric circular nanoplate energy harvesters under pressure is studied. An approximated closed-form solution for electrical energy of the nanoplate is derived by using energy method. Results show that the influence of surface effect on the energy generating performance of piezoelectric circular nanoplate is more significant for a nanoplate with a small thickness and a large radius to thickness ratio of the nanobeam.The influence of surface effect on the nonlinear bending and vibration of electrically actuated nanobeams is studied. The effects of surface energy,midplane stretching and Casimir force are considered simultaneously for a clamped beam. Through differential quadrature method(DQM), the pull-in voltages of nano-switch are obtained. Results show that the effects of surface energy and geometrically nonlinear deformation on the pull-in voltage depend on the length, height and initial gap of the nano-switch. In addition, the effect of Casimir force on the pull-in voltage weakens as the initial gap increases. For a cantilevered nanobeam, a general model for nano-cantilever switches with consideration of surface stress, nonlinear curvature, the location and length of the fixed electrode is developed. Some representative cantilevered switch architectures are incorporated into this model. The governing equation is derived by using Hamilton principal and solved numerically. Results show that the influence of nonlinear curvature and surface effect on the pull-in instability and free vibration is significant for a switch with a larger gap-length ratio and a short fixed electrode(the length of the fixed electrode is smaller than that of the cantilever nanobeam). The length and position of the fixed electrode have a significant effect on the pull-in parameters.Effect of surface energy on the nonlinear bending and vibration of electrically actuated nanoscale plates is analyzed based on the modified couple stress theory. A reduced-order model is derived to consider the geometrically nonlinear strain, surface energy, the Casimir force and the material length scale simultaneously. Results show that the pull-in voltage and fundamental frequency of the plate are considerably enhanced by the material length scale, surface energy and geometrically nonlinear deformation. However, these quantities are weakened with the inclusion of Casimir force. The effects of surface energy and the material length scale become more significant if the thickness of the plate decreases.