Flow Induced Vibration Response And Stability Of Pipe Conveying Fluid And Tube Array

In this dissertation the related problem of flow induced vibration of pipe conveying fluid and tube array is studied. The research mainly includes the several parts:based on the linear dynamical model of pipe conveying fluid, the forced vibration and free vibraton are studied by the green function method and He's varational iteration method, respectively. The nonlinear dynamic of cantilvered pipe conveying pulsating fluid on the elastic foundation is studied. The effects of some parametric variation on the nonlinear dynamical behavior of system are examined. Furthermore, the stability and nonlinear dynamical behavior of slightly curved pipe conveying pulsating fluid are analyzed. Finally, the stability and nonlinear response of a single elastic tube of a tube array in cross flow are studied. The main contributions of this dissertation are:1. Based on the Green function, a new method of investigating the forced vibrations of pipe conveying fluid is presented. The Green functions for pipes with different homogenous and elastic boundary conditions are obtained.The proposed method provides the exact solutions of pipe conveying fluid in closed form, the results of which show that the Green function method is an efficient means of analyzing the natural frequencies and the forced vibration of pipes conveying fluid.2. He's variational iteration method (HVIM) is applied to analyze the free vibration of pipe conveying fluid. The critical flow velocity and frequencies of the conveying fluid pipe with various boundary conditions are obtained. The calculated results of HVIM are compared with those of the Different transform method (DTM), which shows that HVIM has the same precision as DTM. The modal shapes of the cantilevered pipe and the pipe with elastic support at both ends in different flow velocity are shown.3. The motion equation of cantilevered pipe conveying pulsating fluid on the non-linear elastic foundation is constructed, which is discretized into ordinate different equations by the Galerkin method. The effects of the parameters including mean flow velocity, fluctuation amplitude, fluctuation frequency and shear stiffness on the nonlinear behaviors of system are studied by the numerical method. The results show much richer dynamical behaviors of the pipe conveying fluid, such as period motion, quasi-period motion and chaotic motion. Furthermore, the foundation shear stiffness can suppress the period motion and chaotic motion of system. With shear stiffness increasing, the chaos state of system gradually changed into periodic motion until the stable state is obtained.4. The nonlinear governing motion equation of a slightly curved pipe with conveying pulsating fluid is set up by the Hamilton's principle. The motion equation is discretized into a set of low dimensional system of nonlinear ordinary differential equations by the Galerkin method. Linear analysis of the system is performed upon this set of equations so as to investigate the effect of the amplitude of the initial deflection and flow velocity. The curves of the resonance responses at ???1 and ??2?1 are performed by means of the pseudo-arclength continuation technique. The global nonlinear dynamic of system is analyzed by establishing the bifurcation diagrams. The dynamical behaviors are identified by the phase diagram and Poincare maps. The periodic motion, chaotic motion and quasi-periodic motion are found in this system.5. The nonlinear behaviors of the slender cylinder with loose support in cross flow are studied. The partial differential motion equation of slender cylinders in cross flow is reduced to series of ordinary differential equations using the Differential Quadrature Method (DQM). By means of the bifurcation diagram and phase portraits of the motion, the effects of parameter variation on the system responses are analyzed. The results show that the parameter region of periodic and chaotic motion are found, which agreed reasonably with other classical ones. The motion equations of time-delay dynamics systems may be discerned by the DQM.6. The nonlinear dynamics of a single elastic cylinder of a cylinders array with general elastic support at its both ends subjected to cross flow is studied. The governing equations of motions are established considering the effect of the axil force on the later deflection. The stability and the nonlinear behavior of the system with different parameter conditions are analyzed. The results show that the initial axil force decrease the stability of the cylinder system, and the system undergos periodic motion and quasi-periodic motion when flow velocity increasing, but there is no chaotic motion in the system.7. The cross-flow-induced vibration of a single elastic cylinder of a cylinder array in thermal environment is researched. The partial differential equation of the system was reduced to an ordinary differential equation by the Galerkin's method. The influence of thermal load on the system critical flow velocity was analyzed, and the bifurcation region of the system and its distribution in the parameter space are obtained by the numerical method. The character of motion was discriminated by the application of the bifurcation diagram and phase portraits. The results show the svstem with changing parameters appears a periodic motion, and the flutter critical flow velocity decreases with increasing temperature. When the temperature load keeps constant, the system goes through limit cycle oscillation, periodic-1 motion. quasi-periodic and chaotic motion with increasing flow velocity.