The effect of small scale and intermolecular forces on the nonlinear Pull-in instability behavior of nano-switches using differential quadrature method

Using differential quadrature method (DQM), this study investigated pull-in instability of beam-type nano-switches under the effects of small-scale and intermolecular forces including the van der Waals (vdW) and the Casimir forces. In these nano-switches, electrostatic forces served as the driving force, and von-Karman type nonlinear strain was used to examine nonlinear geometric effects. To derive nonlinear governing equations as well as the related boundary conditions for the nano-beam, variation method was used. Besides, to study the influence of size effect, the nonlocal elasticity theory was employed and the resulting governing equations were solved using DQM. Finally, the pull-in parameters were studied using the nonlocal theory and the results were compared with the numerical results of the classical continuum theory as well as experimental results contained in the references. Results demonstrated that taking into consideration the von-Karman type nonlinear strain increases the beam stiffness and hence, the pull-in voltage. Besides, use of the small scale, compared with the classical theory of elasticity, yields results much closer to experimental results.