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    Intermittency Route to Chaos of a Cantilevered Pipe Conveying Fluid With a Mass Defect at the Free End

    Source: Journal of Applied Mechanics:;1995:;volume( 062 ):;issue: 004::page 903
    Author:
    C. Semler
    ,
    M. P. Païdoussis
    DOI: 10.1115/1.2896019
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: The nonlinear equations for planar motions of a vertical cantilevered pipe conveying fluid are modified to take into account a small lumped mass added at the free end. The resultant equations contain nonlinear inertial terms; by discretizing the system first and inverting the inertia matrix, these terms are transferred into other matrices. In this paper, the dynamics of the system is examined when the added mass is negative (a mass defect), by means of numerical computations and by the software package AUTO. The system loses stability by a Hopf bifurcation, and the resultant limit cycle undergoes pitchfork and period-doubling bifurcations. Subsequently, as shown by the computation of Floquet multipliers, a type I intermittency route to chaos is followed—as illustrated further by a Lorenz return map, revealing the well-known normal form for this type of bifurcation. The period between “turbulent bursts” of nonperiodic oscillations is computed numerically, as well as Lyapunov exponents. Remarkable qualitative agreement, in both cases, is obtained with analytical results.
    keyword(s): Fluids , Pipes , Chaos , Bifurcation , Computation , Computer software , Cycles , Equations , Nonlinear equations , Automobiles , Motion , Turbulence , Inertia (Mechanics) , Oscillations , Dynamics (Mechanics) AND Stability ,
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      Intermittency Route to Chaos of a Cantilevered Pipe Conveying Fluid With a Mass Defect at the Free End

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    contributor authorC. Semler
    contributor authorM. P. Païdoussis
    date accessioned2017-05-08T23:46:16Z
    date available2017-05-08T23:46:16Z
    date copyrightDecember, 1995
    date issued1995
    identifier issn0021-8936
    identifier otherJAMCAV-26366#903_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/114759
    description abstractThe nonlinear equations for planar motions of a vertical cantilevered pipe conveying fluid are modified to take into account a small lumped mass added at the free end. The resultant equations contain nonlinear inertial terms; by discretizing the system first and inverting the inertia matrix, these terms are transferred into other matrices. In this paper, the dynamics of the system is examined when the added mass is negative (a mass defect), by means of numerical computations and by the software package AUTO. The system loses stability by a Hopf bifurcation, and the resultant limit cycle undergoes pitchfork and period-doubling bifurcations. Subsequently, as shown by the computation of Floquet multipliers, a type I intermittency route to chaos is followed—as illustrated further by a Lorenz return map, revealing the well-known normal form for this type of bifurcation. The period between “turbulent bursts” of nonperiodic oscillations is computed numerically, as well as Lyapunov exponents. Remarkable qualitative agreement, in both cases, is obtained with analytical results.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleIntermittency Route to Chaos of a Cantilevered Pipe Conveying Fluid With a Mass Defect at the Free End
    typeJournal Paper
    journal volume62
    journal issue4
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.2896019
    journal fristpage903
    journal lastpage907
    identifier eissn1528-9036
    keywordsFluids
    keywordsPipes
    keywordsChaos
    keywordsBifurcation
    keywordsComputation
    keywordsComputer software
    keywordsCycles
    keywordsEquations
    keywordsNonlinear equations
    keywordsAutomobiles
    keywordsMotion
    keywordsTurbulence
    keywordsInertia (Mechanics)
    keywordsOscillations
    keywordsDynamics (Mechanics) AND Stability
    treeJournal of Applied Mechanics:;1995:;volume( 062 ):;issue: 004
    contenttypeFulltext
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