## Spatial parametrical vibrations of a pipeline affected by variable internal pressure. Part I

During transportation of crude oil and refined products for long distances the above-ground segments of a pipeline, in their passage through such obstacles as mountains, water bodies, communications, etc., get bent by gravity and can execute spatial vibrations under the effect of alternating internal pressure. Pipeline vibrations can be stronger or weaker depending on certain relationships among parameters. Thus, an investigation into pipeline spatial vibrations is of much topicality and practical importance. Consideration is given to spatial vibrations of a pipeline with liquid contained in it about the horizontal axis that passes through bearings. In a steady state the pipeline is bent by gravity and is affected by internal pressure. The elasticity coefficients of the bearings and deformations of the pipeline associated with its exit out of the bending plane are reckoned as small; therefore the pipeline bent axis represents a planar curve. In this case, one should allow for inertial Coriolis forces, buoyancy force and drag force proportional to the first-order velocity. Based on the obtained model we have developed a set of two nonlinear differential equations for the pipeline flexural and rotational vibrations solved with the aid of the sequentially applied Bubnov-Galerkin and Runge-Kutta methods. Free vibrations of the pipeline have been examined. Computational results for actual values of the key parameters are given in the form of diagrams. General conclusions are presented in the work.

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parametrical; pipeline; spatial; variable internal pressure; vibrations; колебания; параметрические; переменное внутреннее давление; пространственные; трубопровод References to this article (GOST) A.G. Khakimov, M.M. Shakiryanov. Spatial parametrical vibrations of a pipeline affected by variable internal pressure. Part I // Electronic scientific journal "Oil and Gas Business". 2011. №6. P.130-146. URL: http://ogbus.ru/authors/KhakimovAG/KhakimovAG_1.pdf