Surface effects on nonlinear free vibration of nanobeams

The nonlinear flexural vibrations of micro- and nanobeams in presence of surface effects are studied within the framework of Euler-Bernoulli beam theory including the von Kármán geometric nonlinearity. Exact solution is obtained for the natural frequencies of a simply-supported nanobeam in terms of the Jacobi elliptic functions by using the free vibration modes of the corresponding linear problem. Numerical results include the normalized natural frequencies of vibration as functions of mode number, vibration amplitude, and nanobeam length and thickness. Also, the influence of surface effects on the system phase trajectory is considered.