Vibration Analysis of Fluid-conveying Carbon Nanotubes with Laminar and Turbulent Flows

In this paper, the free vibration and divergence instability of single-walled carbon nanotubes conveying fluid with considering the effects of non-uniformity of laminar and turbulent flow velocity distribution are investigated based on nonlocal elasticity theory. The non-uniform flow velocity distribution occurs due to the viscosity of the fluids. Based on the Euler-Bernoulli beam theory, the governing equations of motion and boundary conditions are derived by using the Hamilton's principle. The centrifugal force term in the equation of motion of the nonotubes is modified for laminar and turbulent flow profiles. The differential transformation method (DTM) is used to solve the governing differential equations of motion. In vibrational analysis the effects of nonlocal parameter and non-uniform flow velocity on the vibrational properties of the carbon nanotubes with different boundary conditions are investigated. Results show that the effects of nonlocal elasticity may increase the natural frequency and critical divergence flow velocity of systems, while the non-uniform flow velocity decreases the critical divergence flow velocity and natural frequency of nanotube, compared to the uniform case. The validity of the present analysis is confirmed by comparing the results with those obtained in literature.