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

Document Type: Research Paper


1 Department of Mechanical Engineering, University of Guilan

2 Department of mechanical engineering, University of Guilan


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


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