Dynamics of fluid conveying pipes using Rayleigh theory under non-classical boundary conditions

With the impact of globalization, transport routes are constantly evolving in recent years depending on such criteria as cost, efficiency, speed and safety. The most important of these transport routes are pipelines. It is of great importance to analyze the dynamic behavior of pipelines built for the transport of crude oil and refined petroleum products, and to project new ones according to the results obtained. The dynamic behaviour of fluid conveying pipe has been investigated by using Rayleigh theory to present the effect of non-classical boundary conditions on natural frequencies. The assumption of ideal fluid is used for acquiring the equation of motion for a uniform Rayleigh pipe. The ideal fluid moves with pipe and the pipe makes small oscillations by Hamilton's variation principle. Euler equation is adopted for the modelling of the flow behaviour in the pipe. Accordingly, the dimensionless partial differential equations of motion are converted into matrix equations and solved for three different set of non-classical boundary conditions. The natural frequencies are obtained analytically depending on fluid velocity and stiffnesses of boundary conditions. The effect of mass ratio, slenderness ratio and damping coefficient on vibration frequency is examined for the first three modes. It have been shown that the boundary conditions and pipe models have strongly important effect on the dynamics and stability of pipes conveying fluid.