Free vibration analysis of micropipe conveying fluid by wave method

The wave method for free vibration analysis of single-wall nanotube conveying fluid is proposed in this paper. The lateral vibration model of nanotube conveying steady flow is derived based on the Timoshenko beam theory. The control partial differential equations are dealt with Fourier transform and the wave form solutions are obtained. The wave propagation matrix and reflection matrices at different boundary conditions are gained. By using the wave train closure principle, the wave characteristic equation for natural frequency computation of nanotube conveying fluid is established. In the example, the natural frequencies of simply supported pipe conveying fluid and the critical velocity of simply supported nanotube conveying fluid are computed and the results show great agreement with that in existing literature. The first five natural frequencies of simply supported and clamped-pinned nanotube conveying fluid are also obtained by the wave method. The influence of fluid velocity on the natural frequency of nanotube conveying fluid is discussed.

► The wave method for free vibration analysis of nanotube conveying fluid is proposed.
► The natural frequency of nanotube with different boundary conditions is computed.
► The effect of fluid velocity on natural frequency of nanotube conveying fluid is discussed.