In this paper, the vibration analysis of carbon nanotubes (CNTs) conveying nanofluid and resting on an elastic foundation is studied based on the nonlocal Timoshenko beam model. Both Winkler type and Pasternak type models are considered to simulate the interaction be- tween the nanotube and the elastic foundation. Moreover, the effects of the inner and outer surface layers on the CNT walls and the small-size effect of the nanoflow are incorporated. The natural frequencies and the critical flow velocity at which instability occurs are obtained using Differential Quadrature Method (DQM). The validation of the present solution method is confirmed by comparing the results with those obtained from literature. Furthermore, the rapid convergence of DQM results proves the suitability, reliability and rapidity of DQM. The effects of the main parameters on the vibrational characteristics of the CNT are also in- vestigated. The present model is absent in the literature which could include the above pa- rameters for the vibration and instability of the CNT conveying fluid.

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