Nonlinear vibrations of planar curved pipes conveying fluid

•The natural vibrations of planar curved tubes are tested.•Experiments confirming the correctness of the extensible centreline theory.•Parametric vibrations in the ranges of simple and combination resonances are excited.•Sub-harmonic and quasi-periodic vibrations can arise in the resonance ranges.•Out-of-plane parametric vibrations are more easily excited. The study investigates the dynamic behaviour of curved pipes in the shape of circular arcs conveying fluid. The effects of flow velocity and tube curvature on vibration modes and natural frequencies are analysed recalling the linear model of the system. A good agreement is observed between experimental results and theoretical predictions based on the model assuming pipe centreline to be extensible. To analyse the vibration due to pulsating flow, the additional non-linear component of the axial force was included and the model of the system was modified accordingly. Instability ranges were determined by the Floquet method a detailed analysis of the non-linear model was performed. The analysis of time histories, phase portraits, motion trajectory, vibration modes, spectral analysis was carried out and bifurcation diagrams were prepared. The effects of pulsation frequency and amplitude, as well as flow velocity, on the range and type of excited parametric vibration were established for pipes with varied curvature. The possibility of simple parametric resonance of single modes as well as combination resonance was confirmed. Calculation results are verified by experiments investigating various forms of parametric resonances.