Size-dependent vibration of fluid-conveying double-walled carbon nanotubes using couple stress shell theory

This work investigated vibrations and instability of double-walled carbon nanotube (DWCNT) conveying fluid by a modified couple stress theory. For this purpose, Donnell's shell model was developed and, using the modified couple stress theory, the equations of motion and corresponding classical and non-classical boundary conditions of DWCNT were obtained through Hamilton's principle. Then, DWCNT with simple-simple and clamped-clamped supports were investigated. The effect of the van der Waals (vdW) forces was considered between the two walls, and the DWCNT surroundings were modeled as a visco-Pasternak foundation. The governing equations of motion and corresponding boundary conditions were discretized through differential quadrature method (DQM), and the vibration problem was solved by using the boundary conditions. The results show that the effects of fluid velocity, stiffness and damping of the visco-Pasternak foundation, nanotube length, and size parameter in the modified couple stress theory are stronger than in the classical theory. Finally, the effect of vdW forces and presence of fluid in the DWCNT examined on the natural frequencies of DWCNT. (C) 2014 Elsevier B.V. All rights reserved