On the torsional vibrations of restrained nanotubes embedded in an elastic medium

Abstract

In this paper, torsional dynamics of nanotubes embedded in an elastic medium with arbitrary elastic boundary conditions is studied. The proposed mathematical model in this study developed based on the nonlocal elasticity theory gives us opportunity to include small-scale parameter. Two springs in torsional direction are attached to a nanotube at both boundaries. Angular rotation function based on the nonlocal elasticity theory is represented by a Fourier sine series. A coefficient matrix including torsional effects is obtained by using Stoke transformation and nonlocal boundary conditions. This coefficient matrix can be used to obtain the torsional vibration frequencies with restrained or rigid (fixed-free) boundary conditions. In order to validate the performance of the present analytical method, results calculated for rigid boundary cases (fixed-free) are presented for a comparison with those given in the literature, and the results agree with each other exactly. It is shown that nonlocal parameter, torsional spring coefficients and elastic medium have a notable impact on the torsional dynamics of carbon nanotubes.