Torsional Vibration and Static Analysis of the Cylindrical Shell Based on Strain Gradient Theory

Abstract

In this paper, the free vibration and torsional static analysis of cylindrical shell are developed using modified strain gradient theory. In doing this, the governing equations and classical and non-classical boundary conditions are derived using Hamilton’s principle. After obtaining equations governing the problem, the differential quadrature method is used to discretize the equations of motion of the vibration problem and to examine the single-walled carbon nanotube (SWCNT) with two clamped-free and clamped–clamped supports as a special application of this formulation. Also, torsional static analysis is carried out for the clamped–clamped SWCNT. Results reveal that SWCNT rigidity in strain gradient theory is higher than that in couple stress theory or the classical theory, which leads to increase in torsional frequencies and decrease in torsion of SWCNT. Results also demonstrate that the effect of size parameter and SWCNT torsion in different lengths and diameters is considerable.