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

Abstract

Abstract The dynamic behavior 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 in the vertical direction with pipe and the pipe makes small oscillations by Hamilton’s variation principle. Euler equation is adopted for the modeling of the flow behavior in the pipe. Accordingly, the dimensionless partial differential equations of motion are converted into matrix equations and solved for two different set of non-classical boundary conditions. The natural frequencies are obtained depending on fluid velocity and stiffnesses of boundary conditions by using Rayleigh Theory. The effect of mass ratio and slenderness ratio on vibration frequency is examined for the first three modes. The one-way FSI (Fluid–Structure Interaction) technique is used by ANSYS software to determine natural frequencies of pipe. The results of first natural frequency based on the numerical solution performed by using ANSYS-FSI are compared with the results of analytical solution for Rayleigh pipe.