The problems of oscillations of a viscoelastic pipeline conveying fluid flow are considered in the paper. Mathematical models of these problems are constructed in a one-dimensional statement. The motion of a pipeline completely filled with a flowing fluid is studied. The transverse oscillations of a pipeline interact with the pipe walls, changing the nature of system oscillations. It is assumed that a pulsating fluid flows in the pipeline. Though the effect of flowing fluid on the pipe motion is considered in the paper, the effect of the pipe on fluid flow is not taken into account here. The mathematical model of the problem is described by the systems of partial integro-differential equations (IDE) with corresponding initial and boundary conditions. Partial IDE obtained using the Bubnov-Galerkin method under considered boundary conditions are reduced to solving ordinary IDE systems with constant coefficients relative to time function. The integration of systems of equations obtained on the basis of a polynomial approximation of deflections was carried out numerically. Based on this method, the algorithms are developed for numerically solving one-dimensional problems of oscillation and stability of viscoelastic pipes conveying fluid flow. It was found that an increase in internal pressure parameter leads to a decrease in critical flow rate. It was shown that an increase in the singularity parameter and the rigidity parameter of continuous layer of a base leads to an increase in critical flow rate. It was revealed that an increase in transverse stationary external load leads to an increase in the amplitude of pipe oscillations.
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