Investigating Nonlinear Vibration of a Fully Clamped Nanobeam in Presence of the van der Waals Attraction

In this paper, combination of the Galerkin decomposition procedure and homotopy analysis method (HAM) is utilized to derive analytical approximate solutions for nonlinear vibration of a fully clamped nanobeam used in the applications of nano-electromechanical systems (NEMS), under the effect of van der Waals (vdW) force. The model accounts for the inherent nonlinearity of distributed vdW force and geometrical nonlinearity of von Karman mid-plane stretching as well as the influence of applied axial loading. The HAM is also optimized to accelerate the convergence of approximate solution. The present results are found to agree well with those obtained by the fourth-order Runge-Kutta method.