USING STRAIN GRADIENT THEORY FOR MODELING THE SIZE-DEPENDENT INSTABILITY or BEAM-TYPE NANO-STRUCTURES IN THE PRESENCE OF CASIMIR FORCE

In recent years, nanostructures have found many applications in variotts engineering branches i.e. mechanics, heat transfer, chemistry, optic, electrics, etc.. These ultra-small structures are increasingly utilized as the basic elements in developing microI’nano— electromechanical systems (MEMS/NEMS). Herein, the strain gradient continuum theory is used to investigate the size-dependent nonlinear pull-in instability of beam-type nano-structures in the presence of Casimir and electrostatic forces. Most common type of nano-structures i.e. nano-bridge is considered. The von-Kannan nonlinear strain is applied to derive the constitutive equation of the beams. Effect of Casimir force is considered in the nonlinear governing equations of the systems. An analytical differential transformation method (DTM} is employed to solve the nonlinear differential equations as well as the numerical solution. Effect of Casimir attraction and the size dependency and the importance of coupling between them on the instability perfonnance are discussed. Moreover, the pull-in parameters i.e. critical tip- delleetion and instability voltage of the nanostructures are determined.

کلیدواژه ها:

Strain gradient theory ، Pull-in instability ، Size effect ، Casimir force ، Differential transfonnation method