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

In this research, in uences of intermolecular interactions on the behavior of nanobeams are studied. Suddenly applied voltages actuates the clamped-clamped nanobeam. The e ects of electrostatic actuation, intermolecular forces, midplane stretching, the fringing eld e ect and residual stress are considered. Initially, the governing equation is non-dimensionalized, and the partial di erential equation of motion is converted to a nonlinear ordinary di erential equation by means of the Galerkin method. Afterwards, the nonlinear ordinary di erential 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 e ects of various parameters on the nonlinear frequency of the response are studied. The results indicate that the nonlinear frequency of oscillations signi cantly decreases by increasing intermolecular e ects.