Application of the variational iteration method to nonlinear vibrations of nanobeams induced by the van der Waals force under different boundary conditions
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The pull-in instability is one of the most important phenomena which is usually associated with nanobeams when they are used in nanoelectromechanical systems (NEMS). This phenomenon may occur without electrical excitation and depends on different parameters. The aim of this paper is to investigate the nonlinear vibrations and pull-in instability of nanobeams in the presence of the van der Waals (vdW) force without electrical excitation. Utilizing Galerkin's method, the partial differential equation of motion is transferred to a nonlinear ordinary differential equation. Afterwards, the variational iteration method (VIM) is employed to obtain the nonlinear frequency and deflection of the nanobeam. The study is performed on doubly clamped, doubly simply supported and clamped-simply supported boundary conditions. The effects of boundary conditions, axial load, aspect ratio and the vdW force on nonlinear frequency and deflection as well as pull-in instability are discussed in details. In addition, three simple and useful equations are developed for predicting the critical values of the vdW force parameter in terms of axial load and aspect ratio parameters. These equations can be employed to estimate the dimensions of nanobeams before their fabrication and using them in the NEMS devices.