A refinement of a problem solution on small transverse vibrations of a straight section of a pipeline

Small transverse vibrations of a straight section of a pipeline with fluid flow are considered. The pipeline is considered from the standpoint of the Euler-Bernoulli beam theory; and the fluid transported, from the standpoint of the theory of an ideal incompressible fluid based on Euler equations in the spatial formulation. The effect of the heterogeneity of the field of velocities and pressures within a flowing medium, arising during bending vibrations of the pipeline, on the amplitude and frequencies of its resonant transverse vibrations, is investigated.