Effects of nonlocal elasticity and slip condition on vibration and stability analysis of viscoelastic cantilever carbon nanotubes conveying fluid

In this study, effects of nonlocal elasticity and slip condition on free vibration and flutter instability analysis of viscoelastic cantilever carbon nanotubes (CNTs) conveying fluid are investigated. Nonlocal Euler-Bernoulli beam theory is employed to establish the governing equations of motion for the vibrational behavior of CNT. The material property of the CNT is simulated by Kelvin-Voigt viscoelastic constitutive relation. The slip boundary conditions of CNT conveying fluid are considered based on Knudsen number (Kn). The equation of motion and associated boundary conditions are derived by using the extended form of Hamilton's principle. The extended Galerkin method is then employed to discretize the equation of motion and boundary conditions which are then solved to calculate the eigenvalues and critical flutter speeds. Detailed results are demonstrated for the dependence of internal moving fluid, nonlocal parameter, structural damping coefficients and Knudsen number on the dimensionless eigenvalues and flutter boundaries of the cantilever CNT. It can be concluded that the structural damping coefficients and Knudsen number does not have a significant effect on the eigenvalues. However, the results show that the structural damping coefficients, Knudsen number and nonlocal parameter have significant effect on the flutter boundaries of the cantilever CNTs. (C) 2015 Elsevier B.V. All rights reserved.