Wave propagation method for in-plane vibration of curved pipe conveying fluid

The Flügge curved beam was applied to approximate the curved pipe, and the fluid acceleration was deduced. Based on total inextensible assumption, the dynamic equations of in-plane vibration of curved pipe conveying fluid are established. After establishing the wave propagation and reflection matrices, the wave propagation method for calculating the natural frequency of curved pipe's in-plane vibration was proposed. In the example, the critical velocity of a semi-circular pipe with clamped support at both ends was calculated.comparison between the result presented in this paper and corresponding data in existing literature shows good agreement. Finally, the first four natural frequencies of clamped-clamped semi-circular pipe conveying fluid were obtained in six different cases of fluid velocity. The results showed that the increasing fluid velocity can decrease the natural frequencies of pipe, and the first natural frequency vanishes when the fluid velocity increases to a certain value.