Analytical solution to nonlinear behavior of electrostatically actuated nanobeams incorporating van der Waals and Casimir forces

In this research, inuences of intermolecular interactions on the behavior of nanobeams are studied. suddenly applied voltages actuates the clamped-clamped nanobeam. the effects of electrostatic actuation, intermolecular forces, midplane stretching, the fringing field effect and residual stress are considered. initially, the governing equation is non-dimensionalized, and the partial differential equation of motion is converted to a nonlinear ordinary differential equation by means of the galerkin method. afterwards, the nonlinear ordinary differential equation of motion is solved using the homotopy analysis method. to validate the model, the response of a sample beam was compared with that in the relevant literature. finally, the effects of various parameters on the nonlinear frequency of the response are studied. the results indicate that the nonlinear frequency of oscillations significantly decreases by increasing intermolecular eects.