Free vibration of circular nanobeams and nanorings including surface effects and resting on elastic foundations

This paper deals with the free vibration problem with consideration of surface properties of nanorings/arches. The Gurtin-Murdach model is employed for incorporating the surface effects parameters including surface density, surface tension and surface elasticity. However linear and nonlinear elastic foundations, are considered on the curved nanobeam. Simply supported at both ends are assumed as a boundary condition for this case. The analytically Navier solution is employed to solve the governing equation. It is explicitly shown that the vibration characteristics of a nanobeams is significantly influenced by these surface effects. However, it is shown that by increasing the size of thickness of curved nanobeam, the influence of surface effects reduce to zero, and the natural frequency reaches its classical value. Numerical results are presented to serve as benchmarks for future analyses of curved nanobeams.

Keywords:

elastic foundations , Nonlocal elasticity , Differential transformation method , surface effect