### Pull-in Instability Analysis of a Nanocantilever Based on the ‎Two-Phase Nonlocal Theory of Elasticity

Document Type : Research Paper

Authors

1 Department of Bio- and Nanomechanics, Belarusian State University, 4 Nezavisimosti Avenue, Minsk, 220140, Belarus

2 Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia, Via Amendola 2, Reggio Emilia, 42122, Italy‎

Abstract

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.

Keywords

Main Subjects

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