Vibrations of Fluid-Conveying Pipes Resting on Two-parameter Foundation

The problem of vibrations of fluid-conveying pipes resting on a two-parameter foundation model such as the Pasternak-Winkler model is studied in this paper. Fluid-conveying pipes with ends that are pinned-pinned, clampedpinned and clamped-clamped are considered for study. The frequency expression is derived using Fourier series for the pinned-pinned case. Galerkin’s technique is used in obtaining the frequency expressions for the clamped-pinned and clamped-clamped boundary conditions. The effects of the transverse and shear parameters related to the Pasternak- Winkler model and the fluid flow velocity parameter on the frequencies of vibration are studied based on the numerical results obtained for various pipe end conditions. From the results obtained, it is observed that the instability caused by the fluid flow velocity is effectively countered by the foundation and the fluid conveying pipe is stabilized by an appropriate choice of the stiffness parameters of the Pasternak-Winkler foundation. A detailed study is made on the influence of Pasternak-Winkler foundation on the frequencies of vibration of fluid conveying pipes and interesting conclusions are drawn from the numerical results presented for pipes with different boundary conditions.