Static Pull-in Analysis of Capacitive FGM Nanocantilevers Subjected to Thermal Moment using Eringen’s Nonlocal Elasticity

This paper aims to investigate the pull-in phenomenon of functionally graded (FG) capacitive nanocantilevers subjected to an electrostatic force and thermal moment due to an applied voltage and thermal shock considering intermolecular force within the framework of nonlocal elasticity theory to account for the small scale effect. The FG nano-beam is made of mixture of metal and ceramic which the material properties vary continuously through the thickness according to an exponential distribution law (E-FGM). The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanosensors. The nano-beam is modeled assuming the Euler–Bernoulli beam theory and the equations are derived using the equilibrium of an element. A Galerkin-based step by step linearization method has been used to solve the governing static deflection equation. The present solution is validated with existing results reported in previous studies. The effects of temperature change, Van der Waals (VdW) or Casimir force and small scale factor on the five types of FG nano-beams are discussed in detail. The results indicate that VdW/Casimir force and thermal moment reduce the pull-in voltage, however, on the contrary, small scale effect cause to slightly increase the amount of pull-in voltage.