Exact solution for the vibrations of cylindrical nanoshells considering surface energy effect

Abstract

It has been revealed that the surface stress effect plays an important role in the mechanical behavior of<br />structures (such as bending, buckling and vibration) when their dimensions are on the order of<br />nanometer. In addition, recent advances in nanotechnology have proposed several applications for<br />nanoscale shells in different fields. Hence, in the present article, within the framework of surface<br />elasticity theory, the free vibration behavior of simply-supported cylindrical nanoshells with the<br />consideration of the aforementioned effect is studied using an exact solution method. To this end, first,<br />the governing equations of motion and boundary conditions are obtained by an energy-based<br />approach. The surface stress influence is incorporated into the formulation according to the Gurtin-<br />Murdoch theory. The nanoshell is modeled according to the first-order shear deformation shell theory.<br />After that, the free vibration problem is solved through an exact solution approach. To this end, the<br />dimensionless form of governing equations is derived and then solved under the simply-supported<br />boundary conditions using a Navier-type solution method. Selected numerical results are presented<br />about the effects of surface stress and surface material properties on the natural frequencies of<br />nanoshells with different radii and lengths. The results show that the surface energies significantly<br />affect the vibrational behavior of nanoshells with small magnitudes of thickness. Also, it is indicated<br />that the natural frequency of the nanoshell is dependent of the surface material properties.