Nonlinear three-dimensional dynamics of flexible pipes conveying fluids

This paper presents a model which describes the non-planar vibrations of an elastic pipe induced by the pulsations of a flowing fluid. The motion of the pipe has been described by a set of four non-linear partial differential equations with periodically varying coefficients. The analysis has been conducted with the use of Galerkin method by applying functions describing the free vibrations of the beam as the shape functions. Floquet theory has been used to determine the unstable areas. The influence of the flow velocity and the pulsation frequency on the character and modes of vibrations and on the ranges of the increased vibration intensity has been examined. The possibility of the excitation of sub-harmonic and quasi-periodic vibrations in ranges of simple and combination parametric resonances has been proved. The results of experiments which confirm the occurrence of the parametric resonance phenomenon have also been presented.