XU Jian, YANG Qian-biao. Flow-Induced Internal Resonances and Mode Exchange in Horizontal Cantilevered Pipe Conveying Fluid(Ⅱ)[J]. Applied Mathematics and Mechanics, 2006, 27(7): 825-832.
Citation: XU Jian, YANG Qian-biao. Flow-Induced Internal Resonances and Mode Exchange in Horizontal Cantilevered Pipe Conveying Fluid(Ⅱ)[J]. Applied Mathematics and Mechanics, 2006, 27(7): 825-832.

Flow-Induced Internal Resonances and Mode Exchange in Horizontal Cantilevered Pipe Conveying Fluid(Ⅱ)

  • Received Date: 2004-05-25
  • Rev Recd Date: 2006-03-01
  • Publish Date: 2006-07-15
  • Based on the nonlinear mathematical model of motion of a horizontally cantilevered rigid pipe conveying fluid, the 3:1 internal resonance induced by the minimum critical velocity is studied in details. With the detuning parameters of internal and primary resonances and the amplitude of the external disturbing excitation varying, the flow in the neighborhood of the critical flow velocity yields that some nonlinearly dynamical behaviors occur in the system such as mode exchange, saddle-node, Hopf and co-dimension 2 bifurcations. Correspondingly, the periodic motion loses its stability by jumping or flutter, and more complicated motions occur in the pipe under consideration. The good agreement between the analytical analysis and the numerical simulation for several parameters ensures the validity and accuracy of the present analysis.
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  • [1]
    徐鉴,杨前彪.流体诱发水平悬臂输液管的内共振和模态转换(Ⅰ)[J].应用数学和力学,2006,27(7):819—824.
    [2]
    Nayfeh A H,Mook D T.Nonlinear Oscillations[M].New York:Wiley,1979,444—544.
    [3]
    Long R H. Experimental and theoretical study of trans verse vibration of a tube containing flowing fluid[J].Journal of Applied Mechanics,1955,77(1):65—68.
    [4]
    Handelman G H.A note on the transverse vibration of a tube containing flowing fluid[J].Quarterly of Applied Mathematics,1955,13(3):326—330.
    [5]
    Naguleswaran S, Williams C J H.Lateral vibrations of a pipe conveying a fluid[J].Journal of Mechanical Engineering Science,1968,10(2):228—238. doi: 10.1243/JMES_JOUR_1968_010_035_02
    [6]
    Stein R A, Torbiner W M.Vibrations of pipes containing flowing fluids[J].Journal of Applied Mechanics,1970,37(6):906—916. doi: 10.1115/1.3408717
    [7]
    Padoussis M P,Laithier B E. Dynamics of Timoshenko beams conveying fluid[J].Journal of Mechanical Engineering Science,1976,18(2):210—220. doi: 10.1243/JMES_JOUR_1976_018_034_02
    [8]
    Padoussis M P,Lu T P, Laithier B E. Dynamics of finite-length tubular beams conveying fluid[J].Journal of Sound and Vibration,1986,106(2):311—331. doi: 10.1016/0022-460X(86)90321-4
    [9]
    Lee U, Pak C H,Hong S C. The dynamics of piping system with internal unsteady flow[J].Journal of Sound and Vibration,1995,180(2):297—311. doi: 10.1006/jsvi.1995.0080
    [10]
    Holmes P J. Bifurcations to divergence and flutter in flow-induced oscillations: a finite-dimensional analysis[J].Journal of Sound and Vibration,1977,53(4):471—503. doi: 10.1016/0022-460X(77)90521-1
    [11]
    Rousselet J, Herrmann G. Dynamic behaviour of continuous cantilevered pipes conveying fluid near critical velocities[J].Journal of Applied Mechanics,1981,48(6):943—947. doi: 10.1115/1.3157760
    [12]
    Padoussis M P, Li G X. Pipes conveying fluid: a model dynamical problem[J].Journal of Fluid and Structures,1993,7(2):137—204. doi: 10.1006/jfls.1993.1011
    [13]
    Semler C, Li X,Padoussis M P. The non-linear equations of motion of pipes conveying fluid[J].Journal of Sound and Vibration,1994,169(3):577—599. doi: 10.1006/jsvi.1994.1035
    [14]
    Padoussis M P.Fluid-Structure Interactions: Slender Structures and Axial Flow[M].San Diego: Academic Press, 1998,415—430.
    [15]
    XU Jian,CHUANG Kwow-wai,CHAN Henry Shui-ying.Co-dimension 2 bifurcation and chaos in cantilevered pipe conveying time varying fluid with three-to-one in internal resonances[J].Acta Mechanics Solid Sinica,2003,6(3):245—255.
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