Stability of the elastically fixed pipeline

The paper studies stability of a pipeline, which left end is fixed in the elastic hinged support and rests on two additional elastic supports. The perturbed motion equation was solved using the method of solution decomposed into the natural oscillation modes with further use of the Bubnov-Galerkin method procedure. Two options of the rod own shape systems were used: with the elastic supports and fixed only at one end. In the first case, natural frequencies and shapes were determined using the initial parameters method. In the second case, the elastic supports reaction was introduced into the equations using the delta function. The stability region boundary with varying rigidities of the elastic supports was constructed based on the parameter plane characterizing the liquid flow speed and linear mass.

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