Analytical treatment of the nonlinear free vibration of cylindrical nanoshells based on a first-order shear deformable continuum model including surface influences

Surface stresses can significantly affect the mechanical behavior of structures when they are scaled down to deep submicron dimensions. The Gurtin–Murdoch surface elasticity theory has the capability to capture the size-dependent behavior of nanostructures due to the surface stress effect in a continuum manner. The present work is concerned with the application of Gurtin–Murdoch theory to the nonlinear free vibration analysis of circular cylindrical nanoshells with considering surface stress and shear deformation effects. The nonlinear governing equations of motion together with the corresponding boundary conditions are firstly derived using Hamilton’s principle, the first-order shear deformation shell theory and von Kármán’s assumption. An analytical approach is then presented to solve the nonlinear free vibration problem. Selected numerical results are given to illustrate the effects of surface energy on the nonlinear free vibration behavior of shear deformable nanoshells with different material and geometrical parameters. It is shown that there is a large difference between the results of Gurtin–Murdoch theory and those of its classical counterpart for very thin nanoshells.