Application of modified Adomian decomposition method to pull-in instability of nano-switches using nonlocal Timoshenko beam theory

In this paper, the pull-in instability of doubly clamped nano-switches subjected to electrostatic and intermolecular forces are investigated. To this end, using Eringen's nonlocal elsticity theory, the static governing equation of nonlocal Timoshenko beam model is derived. The obtained equation which is a high-order nonlinear ordinary differential equation owing to the electrostatic and intermolecular forces is solved through the use of modified Adomian decomposition method (MADM). This method presents an analytical approximate solution by which the small scale effect on the static pull-in instability of nanobeam is examined. The results obtained from the present method are found to be in reasonable agreement with ones generated by the differential quadrature method (DQM) and experiment. A parametric study is carried out to study the effect of nonlocal parameter on the mid-point deflection, external forces, bending moment and shear force of doubly clamped nanobeams. Moreover, the results of nonlocal Timoshenko beam model are compared with those of nonlocal Euler-Bernoulli and classical beam models.