Influence of surface effect on linear vibrations of multi-walled nanoshell

from the variational approach to describe shell-like vibrations of nanotube. The nonlocal elasticity, Sanders-Koiter shell theory and surface effect are implemented in the nanotube mathematical model. The Galerkin method in the form of weight residual technique is used to transform the PDEs into the system of ordinary differential equations (ODEs) with respect to the generalized coordinates. The parameters of linear vibrations are analyzed from the eigenvalue problem. The influence of surface effect and nonlocal elasticity on the nanotube eigenfrequencyies is studied by using the obtained model. The surface effect affects significantly on the shell-like nanotube eigenfrequencies. These eigenfrequencies are increased, when the surface effect is considered. If nonlocal elasticity is considered, the eigenfrequencies of nanotube are decreased in comparison of nanostructure eigenfrequencies without accounte of nonlocal elasticity.