Vibration analysis of a multi-span fluid conveying pipe with wave propagation method

Based on the Timoshenko beam model, a wave propagation method for vibration analysis of a multi-span fluid conveying pipe is presented in this paper. Utilizing the geometry continuity and force balance condition, the wave reflection models are obtained for fixed-supported, simply-supported and free ends, respectively. The scattering model is established for the intermediate elastic support. In terms of the above scattering model, the frequency characteristic equation is deduced for the multi-span pipe. The correctness of the proposed model is validated by calculating the critical velocity of a simply-supported pipe. Finally, the present method is applied to calculate the first five natural frequencies of a seven span, 40 meters long pipe in three different cases. The results show that the proposed method is convenient for programming and with a high degree of accuracy.