Transient response analysis of multi-span pipe conveying fluid

The method of reverberation-ray matrix proposed by Pao et al. is applied to analyze the transient response of a multi-span pipe conveying fluid. The pipe under transverse vibration is considered as Timoshenko beam conveying axial flow. In the process of analysis, fast Fourier transform is used to convert the partial differential equation into ordinary differential equation. The support points of the pipe are chosen as the elements’ nodes. The transient wave motions at each node are divided into incident and reflected wave. By virtue of continuity and balance condition, the scattering relation is established between the above wave motions. The transient response is obtained by inverse fast Fourier transform. In the examples, the natural frequencies are calculated for single- and multi-span pipe conveying fluid with different fluid velocity, and great agreement is shown with the published literature. And then the transient responses, such as deformation, velocity, shear force and bending moment are obtained for a two-span pipe conveying fluid under different fluid velocity.