pull-in instability analysis of a nanocantilever based on the ‎two-phase nonlocal theory of elasticity

This paper deals with the pull-in instability of cantilever nano-switches subjected to electrostatic and intermolecular forces in the framework of the two-phase nonlocal theory of elasticity. the problem is governed by a nonlinear integro-differential equation accounting for the external forces and nonlocal effects. assuming the helmholtz kernel in the constitutive equation, we reduce the original integro-differential equation to a sixth-order differential one and derive a pair of additional boundary conditions. aiming to obtain a closed-form solution of the boundary-value problem and to estimate the critical intermolecular forces and pull-in voltage, we approximate the resultant lateral force by a linear or quadratic function of the axial coordinate. the pull-in behavior of a freestanding nanocantilever as well as its instability under application of a critical voltage versus the local model fraction are examined within two models of the load distribution. it is shown that the critical voltages calculated in the framework of the two-phase nonlocal theory of elasticity are in very good agreement with the available data of atomistic simulation.