Size-Dependent Large Amplitude Vibration Analysis of Nanoshells Using the Gurtin-Murdoch Model

Shell-type nanostructures have recently attracted a lot of attention due to their several applications. The surface stress effect plays an important role in the mechanical behavior of such structures because of their large surface-to-volume ratio. In this paper, an analytical approach is presented for analyzing the geometrically nonlinear free vibrations of cylindrical nanoshells. In order to capture the surface stress influence, the Gurtin-Murdoch continuum model is applied. First, the equations governing the nonlinear vibrations of the shell considering the surface stress effect are derived using an energy-based method. In the next step, a perturbation technique is utilized to obtain the frequency-amplitude curves of nanoshells. Various numerical results are given to investigate the vibrational behavior of nanoshells with different geometrical and surface material properties. It is shown that the surface stress significantly affects the nonlinear free vibration behavior of the nanoshells when they are very thin. Also, it is revealed that the effect of geometrical nonlinearity is more prominent when the surface residual stress is negative.