Nonlinear free vibration analysis of cylindrical nanoshells based on the Ru model accounting for surface stress effect

In this article, the nonlinear free vibration behavior of circular cylindrical nanoshells is investigated within the framework of surface stress elasticity theory. To accomplish this goal, a nonlinear shell model is developed based upon the model proposed by Ru [Continuum Mech. Thermodyn., 2016, vol. 28, pp. 263-273] and the classical shell theory. The geometric nonlinearity is taken into account using von Kármán's hypothesis. Hamilton's principle is also utilized to derive the governing equations including surface effects. Thereafter, using the multiple scales method, an analytical solution is obtained for the nonlinear free vibrations of simply-supported nanoshells. In the numerical results, the influences of surface stress, initial surface tension, length-to-radius and radius-to-thickness ratios on the vibration characteristics of nanoshells are studied.