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In this paper, the stability of a periodic heterogeneous nanotube conveying fluid is investigated. The governing equations of the nanotube system are derived based on the nonlocal Euler–Bernoulli beam theory. The dynamic stiffness method is employed to analyze the natural frequencies and critical flow velocities of the heteronanotube. The results and discussions are presented from three aspects which reveal the influences of period number, material length ratio and boundary conditions. In particular, we make comparisons between the heterogeneous nanotubes with periodic structure and the homogeneous ones with the same integral values of material properties along the longitudinal direction to isolate the influences of periodic distribution. According to the simulation results, we can conclude that with a proper selection of period number in terms of length ratio, the stability of the constructed nanotube can be improved.

As a hollow cylindrical structure, a nanotube has potential to convey nanoflow, which has opened up a field of research. Functionally graded nanotube as a designable structure with continuous variation of material properties can perform better than uniform nanotube, especially in physical field without introducing large stress concentration. In this article, we take the thermal effect into account and investigated the wave propagation characteristics of functionally graded material nanotube conveying nanoflow. In particular, we compared the effects of different kinds of volume fraction function and also the cases of uniform and nonuniform temperature variation. According to the numerical results, we can conclude that as we decrease the exponent n of the volume fraction function, the system is enhanced and larger enhancement can be observed in the case of the power volume fraction function. In addition, there is a positive correlation between the stability and both the temperature variation and the nonuniformity of temperature variation.

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