The methodology and the results of numerical-analytical study of the non-conservative stability of a cantilever pipeline as a typical hydro-elastic system and of a cantilever rod with a tracking force on the free end are presented. The study was conducted in two ways. The first one is based on representing the solution using the first two rod forms of natural oscillations, whereas the second one is reduced to the exact solution of the eigenvalue problem, as it is not limited by traditionally accounting only for a small number of the lowest oscillation forms. The algorithm is tested by comparing the obtained results with the results of classical and modern numerical and experimental investigations
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