Nonlinear frequency analysis of nanotubes with surface effects

In the current work we obtained exact solution for nonlinear free vibration of nanotubes (NTs) with surface effects incorporated to Euler-Bernoulli beam theory and von Karman geometric nonlinearity. We used Jacobi elliptic functions to obtain the nonlinear natural frequencies. Normalized nonlinear natural frequencies and the phase trajectory were studied with the presence of surface effects. This study might be helpful to design NT-based devices in a wide range of applications.

Keywords:

Nonlinear natural frequency , phase trajectory , surface effect , nanotube