Modified model for instability analysis of symmetric FGM double-sided nano-bridge: Corrections due to surface layer, finite conductivity and size effect

Finite conductivity, size dependency and surface layer are known as crucial factors that affect the electromechanical response and pull-in instability of micro/nano-electromechanical systems (MEMS/NEMS). However, these effects are yet ignored on modeling the instability of MEMS/NEMS fabricated from functionally graded materials (FGMs). Herein, a modified continuum model is developed to incorporate these effects on the dynamic behavior and electromechanical instability of double-sided FGM NEMS bridge. Using Gurtin–Murdoch model in conjunction with nonlocal Eringen elasticity, the governing equations of the nano-bridges is derived considering the surface layer and size dependency. The Coulomb and Casimir forces are incorporated in the governing equation considering the corrections due to the finite conductivity of FGM (relative permittivity and plasma frequency). The validity of the proposed method is elucidated by comparing the results obtained from the present study with the results reported in the literature. The stability analysis of the nanostructure is conducted by plotting time history and phase portraits. The effects of various parameters including finite conductivity, nonlocal parameter, surface stresses and material characteristics on the dynamic pull-in behavior of the nano-bridges are studied. The obtained results imply a significant impact of the abovementioned corrections on the instability threshold and pull-in parameters of the FGM nanobridge.