A Nonlocal Strain Gradient Shell Model for Free Vibration Analysis of Functionally Graded Shear Deformable Nanotubes

Abstract

In the current study, the size dependent free vibration of shear deformable functionally graded (FG) nanotubes is investigated. The nanotube is modeled as cylindrical shell which contains small scale effects by using the nonlocal strain gradient theory. Material properties of the FG nanotube are assumed to be variable along thickness direction according to power law distribution. The Hamilton's principle is implemented to derive the governing equations and boundary conditions. The numerical results are presented for simply supported FG nanotube and the influence of different parameters, such as nonlocal parameter, length scale parameter, length, thickness and power law index on frequency of FG nanotube are extensively studied. The results reveal that the frequency is significantly size dependent.