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

In this research, influences of intermolecular interactions on the behavior of nanobeams are studied. A sudden applied voltage actuates the clamped-clamped nanobeam. The effects of electrostatic actuation, intermolecular forces, midplane stretching, fringing field effect and residual stress are considered. Initially, the governing equation is nondimensionalized and the partial differential equation of motion is converted to a nonlinear ordinary differential equation by means of Galerkin’s method. Afterwards, the nonlinear ordinary differential equation of motion is solved by means of homotopy analysis method. To validate the model, the response of a sample beam was compared with 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 effects.