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    Dynamics of Forced Nonlinear Systems Using Shooting/Arc-Length Continuation Method—Application to Rotor Systems

    Source: Journal of Vibration and Acoustics:;1997:;volume( 119 ):;issue: 001::page 9
    Author:
    P. Sundararajan
    ,
    S. T. Noah
    DOI: 10.1115/1.2889694
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: The analysis of systems subjected to periodic excitations can be highly complex in the presence of strong nonlinearities. Nonlinear systems exhibit a variety of dynamic behavior that includes periodic, almost-periodic (quasi-periodic), and chaotic motions. This paper describes a computational algorithm based on the shooting method that calculates the periodic responses of a nonlinear system under periodic excitation. The current algorithm calculates also the stability of periodic solutions and locates system parameter ranges where aperiodic and chaotic responses bifurcate from the periodic response. Once the system response for a parameter is known, the solution for near range of the parameter is calculated efficiently using a pseudo-arc length continuation procedure. Practical procedures for continuation, numerical difficulties and some strategies for overcoming them are also given. The numerical scheme is used to study the imbalance response of a rigid rotor supported on squeeze-film dampers and journal bearings, which have nonlinear stiffness and damping characteristics. Rotor spinning speed is used as the bifurcation parameter, and speed ranges of sub-harmonic, quasi-periodic and chaotic motions are calculated for a set of system parameters of practical interest. The mechanisms of these bifurcations also are explained through Floquet theory, and bifurcation diagrams.
    keyword(s): Dynamics (Mechanics) , Nonlinear systems , Rotors , Bifurcation , Motion , Algorithms , Dampers , Damping , Spin (Aerodynamics) , Stability , Systems analysis , Stiffness , Journal bearings AND Mechanisms ,
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      Dynamics of Forced Nonlinear Systems Using Shooting/Arc-Length Continuation Method—Application to Rotor Systems

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    http://yetl.yabesh.ir/yetl1/handle/yetl/119751
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    contributor authorP. Sundararajan
    contributor authorS. T. Noah
    date accessioned2017-05-08T23:55:21Z
    date available2017-05-08T23:55:21Z
    date copyrightJanuary, 1997
    date issued1997
    identifier issn1048-9002
    identifier otherJVACEK-28836#9_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/119751
    description abstractThe analysis of systems subjected to periodic excitations can be highly complex in the presence of strong nonlinearities. Nonlinear systems exhibit a variety of dynamic behavior that includes periodic, almost-periodic (quasi-periodic), and chaotic motions. This paper describes a computational algorithm based on the shooting method that calculates the periodic responses of a nonlinear system under periodic excitation. The current algorithm calculates also the stability of periodic solutions and locates system parameter ranges where aperiodic and chaotic responses bifurcate from the periodic response. Once the system response for a parameter is known, the solution for near range of the parameter is calculated efficiently using a pseudo-arc length continuation procedure. Practical procedures for continuation, numerical difficulties and some strategies for overcoming them are also given. The numerical scheme is used to study the imbalance response of a rigid rotor supported on squeeze-film dampers and journal bearings, which have nonlinear stiffness and damping characteristics. Rotor spinning speed is used as the bifurcation parameter, and speed ranges of sub-harmonic, quasi-periodic and chaotic motions are calculated for a set of system parameters of practical interest. The mechanisms of these bifurcations also are explained through Floquet theory, and bifurcation diagrams.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleDynamics of Forced Nonlinear Systems Using Shooting/Arc-Length Continuation Method—Application to Rotor Systems
    typeJournal Paper
    journal volume119
    journal issue1
    journal titleJournal of Vibration and Acoustics
    identifier doi10.1115/1.2889694
    journal fristpage9
    journal lastpage20
    identifier eissn1528-8927
    keywordsDynamics (Mechanics)
    keywordsNonlinear systems
    keywordsRotors
    keywordsBifurcation
    keywordsMotion
    keywordsAlgorithms
    keywordsDampers
    keywordsDamping
    keywordsSpin (Aerodynamics)
    keywordsStability
    keywordsSystems analysis
    keywordsStiffness
    keywordsJournal bearings AND Mechanisms
    treeJournal of Vibration and Acoustics:;1997:;volume( 119 ):;issue: 001
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
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