Vibration and instability analysis of flow-conveying carbon nanotubes in the presence of material uncertainties

This paper aims to present an interval analysis method to reveal the vibration and instability behaviors of flow-conveying CNTs under uncertain material properties. Based on the nonlocal Timoshenko beam theory, the governing equation of a flow-conveying CNT surrounded by a Pasternak-type elastic medium is derived. Firstly, the deterministic parametric analysis is performed to highlight the influence of the material properties on the critical flow velocity and fundamental frequency of the system. Then, these material parameters are all defined as uncertain-but-bounded variables, and the critical flow velocity and the upper and lower bounds of the fundamental frequency of the system are examined correspondingly by using the surrogate model-based interval analysis method. Finally, the effects of elastic medium, nonlocal coefficient and uncertain level on the critical flow velocity and bounds of the fundamental frequency are discussed in detail. In addition, the verification of the proposed method is confirmed by probabilistic method and Monte Carlo simulation. Conclusions obtained in this paper can provide helpful guidelines for the precise control of the flow-conveying CNTs.