The non-linear equations of motion of a #exible pipe conveying unsteadily #owing #uid are derived from the continuity and momentum equations of unsteady #ow. These partial di!erential equations are fully coupled through equilibrium of contact forces, the normal compatibility of velocity at the #uid} pipe interfaces, and the conservation of mass and momentum of the transient #uid. Poisson coupling between the pipe wall and #uid is also incorporated in the model. A combination of the "nite di!erence method and the method of characteristics is employed to extract displacements, hydrodynamic pressure and #ow velocities from the equations. A numerical example of a pipeline conveying #uid with a pulsating #ow is given and discussed.

The dynamic equilibrium matrix equation for a discretized pipe element containing flowing fluid is derived from the Lagrange principle, the Ritz method and consideration of the coupling between the pipe and fluid. The Eulerian approach and the concept of fictitious loads for kinematic correction are adopted for the analysis of geometrically non-linear vibration. The model is then deployed to investigate the vibratory behaviour of the pipe conveying fluid. The results for a long, simply supported, fluid-conveying pipe subjected to initial axial tensions are compared with experimentally obtained results and those from a linear vibration model

No abstract

A study of the eect of axial tension on the vibration of a single-span elastomeric pipe clamped at both ends conveying¯uid has been carried out both experimentally and theoretically. A new mathematical model using a penalty function technique and the method of kinematic correction and ®ctitious loads has been developed. The in¯uence of¯owing¯uid and axial tension on natural frequencies and mode shapes of the system has been described using this model and compared with experimental observations. Linear and non-linear dynamic response of the harmonically excited pipe has also been investigated for varying¯ow velocities and initial axial tensions.