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