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This paper investigates the pull-in instability of nano-switches subjected to an electrostatic force due to an applied voltage and intermolecular force within the framework of nonlocal elasticity theory to account for the small scale effect. Both the nonlinear governing equation and boundary conditions with nonlocal effect are derived. A linear distributed load model is proposed to approximate the nonlinear intermolecular and electrostatic interactions. Closed-form solutions of critical pull-in parameters are obtained for cantilever and fixed–fixed nano-beams. The freestanding behaviour of nano-beams, which is a special case in the absence of electrostatic force, is also studied. It is found that the small scale effect contributes to the pull-in instability and freestanding behaviour of cantilever and fixed–fixed nano-beams in quite different ways. The effects of gap ratio, slenderness ratio and intermolecular force are discussed in detail as well.

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This paper investigates the free vibration characteristics of micro-switches under combined electrostatic, intermolecular forces and axial residual stress, with an emphasis on the effect of geometric nonlinear deformation due to mid-plane stretching and the influence of Casimir force. The micro-switch considered in this study is made of either homogeneous material or non-homogeneous functionally graded material with two material phases. The Euler-Bernoulli beam theory with von Karman type nonlinear kinematics is applied in the theoretical formulation. The principle of virtual work is used to derive the nonlinear governing differential equation. The eigenvalue problem which describes free vibration of the micro-beam at its statically deflected state is then solved using the differential quadrature method. The natural frequencies and mode shapes of micro-switches for four different boundary conditions (i.e. clamped-clamped, clamped-simply supported, simply supported and clamped-free) are obtained. The solutions are validated through direct comparisons with experimental and other existing results reported in previous studies. A parametric study is conducted to show the significant effects of geometric nonlinearity, Casimir force, axial residual stress and material composition for the natural frequencies.

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