Parametric vibrations of flexible hoses excited by a pulsating fluid flow, Part I: Modelling, solution method and simulation

• The effect of various parameters on parametric resonance ranges has been investigated.
• The character and modes of vibrations have been investigated.
• Parametric vibrations can arise in the simple and combination resonance ranges.
• Periodic, sub-harmonic and quasi-periodic vibrations are induced.
• The analysis methods employed allow efficient qualitative analyses in a short time.

The article presents an analysis of a model describing lateral vibrations of a pipe induced by fluid flow velocity pulsation. The motion has been described with a set of two non-linear partial differential equations with periodically variable coefficients. In the analysis Galerkin method has been applied using orthogonal polynomials as shape function. To determine instability regions Floquet theory has been employed. The effect of selected parameters on parametric resonance ranges and regions of increased vibration level has been investigated. The character and form of vibrations have been investigated indicating the possibility of excitation of sub-harmonic and quasi-periodic vibrations in the combination resonance ranges.