Size-dependent frequency of simply supported elastic ultra-thin films with surface effect under periodic vibration

Abstract

Although surface effects play an important role in the mechanical properties of ultra-thin films, the nonlinear vibrations of ultra-thin films influenced by surface effects have not been fully understood. This paper develops an analytical framework for studying the nonlinear vibrations of simply supported ultra-thin films with surface effects. The framework is based on the modified Kirchhoff plate theory. The surface stress effects are treated by the Gurtin–Murdoch surface elasticity model and the motion equations include the effects of curvature and classical inertia. The dimensionless frequency of forcibly vibrated ultra-thin films with a simple support and surface effects is explicitly deduced through a series of perturbation procedure. Finally, the surface effects are evaluated in two numerical examples. In these demonstrations, the surface effects significantly influenced the dimensionless frequency when the film thickness reduced to one micrometer or less.