Higher-order vibration analysis of FG cylindrical nano-shell

This paper investigates vibration responses of cylindrical nano-shell using the higher-order shear deformation theory. Small scale is considered using the Eringen nonlocal elasticity theory. The cylindrical nano-shell is assumed that made from functionally graded materials in which power-law distribution is used. For more accurate modeling the nano-shell, displacement field components are developed based on third-order shear deformation theory including radial and axial displacements along the thickness direction. Constitutive relations are developed based on generalized Hooke’s law with accounting transverse shear strain and three normal strain components. After derivation of governing equations of motion, an exact solution is proposed for solution of them for simply supported boundary conditions. The natural frequencies are evaluated in terms of significant material and geometric parameters in graphical form. Investigating effect of various parameters on the obtained results reflects this conclusion that the natural frequencies are decreased with increase of in-homogeneous index and nonlocal parameter. Furthermore, increase in both parameters of foundation leads to increase of natural frequencies.