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Dynamic response of offshore pipelines and risers under cross-flow (e.g. ocean currents, vessel motion etc.) has successfully been analysed. Although the pipelines are used for fluid transportation, sufficient attention has not been paid to the dynamic instability under axial flow. In this study, axial flow-induced instability mechanisms of offshore pipelines and risers are investigated. To this end, the interaction of the axial flow forces of a fluid element with the forces of the corresponding pipe element during pipeline flexural motion is analysed. Interpretation of the terms of the motion equation is provided and analogies with the model of dynamic buckling of a Euler beam are detected. Original transfer matrices are developed for the dynamic control of pipelines under axial flow. The critical values of the flow velocity causing dynamic instability and the corresponding axial flow-induced buckling modes are determined. Implementation of the method to a representative case study is provided and discussed.

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