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The paper presents a numerical and analytical investigation of the stability of a cantilevered pipeline transporting an incompressible fluid flow at a constant speed compressed by tracking force at the free end. To solve the problem, a dynamic approach based on the analysis of the behavior of the system’s own characteristics is used. In contrast to the classical research approaches, which are based on the representation of the solution of the problem using a finite number of basic functions, an algorithm that does not require such a restriction is proposed.

Investigation of the stability of a cantilevered pipeline with a fluid flow compressed at the free end by the tracking force