A coupled problem of hydroelasticity consisting of dynamic equations of a viscous incompressible liquid and dynamic equations of interior and external elastic cylindrical shells of final length, based on hypotheses of the Kirchhoff - Love, with the corresponding boundary conditions is formulated and solved for a harmonic modification of the inlet and outlet pressure of an elastic pipe of the ring cross-section. From the solution of this problem, parameters of the flow and elastic displacements of the shells are determined. Their amplitude and phase frequency characteristics and resonance frequencies are found. Cases of simply supported and rigidly clamped at the ends shells are analyzed, as well as the effect of the type of fixing and of the properties of the fluid on resonance frequencies and amplitude frequency characteristics of the shells.
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