Nonlinear Dynamics Of Transverse Vibrations Of Pipes Conveying Fluid In The Supercritical Regime

Pipes conveying fluid are present in various industrial applications such aslubrication pipes in aeronautical engineering, hydraulic oil pipes in astronauticalengineering, boiler pipes in marine engineering and heat exchanger tube bundles innuclear reactors. The problem of pipes conveying fluid belongs to the broader class ofproblems involving axially moving continua, as in other applicatios like the context ofgyroscopic systems. The study of the vibration response of the fluid-structure is of greatsignificance.If the flow speed is larger than the critical value, the supported pipes with internalradii less than their length becomes unstable. The straight equilibrium configurationbifurcates into two possible curved equilibrium configurations. Under the supercriticalflow assumptions, the governing equations for finite local motion about each bifurcatedsolution are cast in the nonlinear integro-paritial-differential equation with variablecoefficients. The equation is truncated into a discreate perturbed gyroscopic system viathe Galerkin method. The perturbation technique and the numertrical method aredeveloped to present the supercritical nonlinear dynamics of transverse vibrations ofpipes conveying fliud. Over the supercritical flow speed range, the free nonlinearviberation of pipes, weak and strong force oscillations of pipes, and paraterically excitedpipes are investigated in detail. The supercritical nonlinear dynamical of the transversemotion of pipes highlight the effects of internal resonance in the dissertation.In the supercritical regime, the disturbance equation of free transverse vibrations ofpipes conveying fluid is derived from the free governing equation via a coordinatetransform. The Galerkin method is applied to truncate the gyroscopic systems. Acondition for two-to-one internal resonance is established in the supercritical regime.The method of multiple scales is applied to obtain the steady-state relationship between the amplitudes in the first two resonant modes.Nonlinear weak forced vibration of a viscoelastic pipe conveying fluid around thecurved equilibrium resulting from the supercritical flow speed is investigated with theemphasis on local dynamics behavior of external and internal resonance. The method ofmultiple scales is developed to present the solvability condition of approximatesolutions. The first two primary resonance of vibration in the presence of two-to-oneinternal resonances are examined. The amplitude double-jumping, softening-spring,hardening-spring, hysteresis and saturation phenomenon are demonstrated. Especially, itis found that a softening spring is changed into a hardening spring when the velocity(linear parameters) gradually approach to the neighborhood of internal resonance.The supercritical nonlinear vibration of fluid-conveying pipes subjected to a strongtransverse external harmonic excitation is investigated for the cases where the system istuned to a two-to-one internal resonance. The method of multiple scales is applied toestablish approximate solutions. For the system in the supercritical regime, thesubharmonic, superharmonic and combination resonances are examined in the presenceof an internal resonance. The jump phenomenon of various resonances are demonstratedin the supercritical regime.The nonlinear dynamics of pipes conveying pulsating fluid near a two-to-oneresonance are investigated in the supercritical regime. The pipe conveys fluid at avelocity with a harmonically varying component over a constant mean velocity. Theparametric excited pipes become the combined parametric and forcing exciataions dueto introducing dynamical coordinate transform. The method of multiple scales isdeveloped to search for approximate solutions.The subharmonic, superharmonic andcombination resonances due to the combined parametric and forcing exciataions areexamined in the presence of an internal resonance. The jump phenomenon of variousresonances under combined parametric and forcing exciataions are presented.The nonlinear dynamical of high-dimensional systems due to the four Galerkintruncation is develop to explore the weak forced vibration of a viscoelastic pipe conveying fluid around the curved equilibrium resulting from the supercritical flowspeed. The four-dimensional solvability condition for the gyroscopic system confirm thenonlinear viberation of the pipes with internal resonance in two-dimensional systems.A wide array of dynamical behavior is observed illustrating the influence of theparameter due to the modal interaction. The steady-state responses and their stability ofthe pipe are determined in the sense of the frequence-response and amplitude-responsecurves. The special examples are presented to highlight the effects of viscoelastic,external amplitude, nonlinearity and flow speed in the supercritical regime. Finally,numerical simalations are carried out to confirm the theoretical results obtained.