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    An Approximate Solution for Period 1 Motions in a Periodically Forced Van Der Pol Oscillator

    Source: Journal of Computational and Nonlinear Dynamics:;2014:;volume( 009 ):;issue: 003::page 31001
    Author:
    Luo, Albert C. J.
    ,
    Baghaei Lakeh, Arash
    DOI: 10.1115/1.4026425
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: In this paper the approximate analytical solutions of period1 motion in the periodically forced van der Pol oscillator are obtained by the generalized harmonic balance (HB) method. Such an approximate solution of periodic motion is given by the Fourier series expression, and the convergence of such an expression is guaranteed by the Fourier series theory of periodic functions. The approximate solution is different from traditional, approximate solution because the number of total harmonic terms (N) is determined by the precision of harmonic amplitude quantity level, set by the investigator (e.g., AN≤ة› and ة›=108). The stability and bifurcation analysis of the period1 solutions is completed through the eigenvalue analysis of the coefficient dynamical systems of the Fourier series expressions of periodic solutions, and numerical illustrations of period1 motions are compared to verify the analytical solutions of periodic motions. The trajectories and analytical harmonic amplitude spectrum for stable and unstable periodic motions are presented. The harmonic amplitude spectrum shows the harmonic term effects on periodic motions, and one can directly know which harmonic terms contribute on periodic motions and the convergence of the Fourier series expression is clearly illustrated.
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      An Approximate Solution for Period 1 Motions in a Periodically Forced Van Der Pol Oscillator

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    http://yetl.yabesh.ir/yetl1/handle/yetl/154166
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    • Journal of Computational and Nonlinear Dynamics

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    contributor authorLuo, Albert C. J.
    contributor authorBaghaei Lakeh, Arash
    date accessioned2017-05-09T01:05:55Z
    date available2017-05-09T01:05:55Z
    date issued2014
    identifier issn1555-1415
    identifier othercnd_009_03_031001.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/154166
    description abstractIn this paper the approximate analytical solutions of period1 motion in the periodically forced van der Pol oscillator are obtained by the generalized harmonic balance (HB) method. Such an approximate solution of periodic motion is given by the Fourier series expression, and the convergence of such an expression is guaranteed by the Fourier series theory of periodic functions. The approximate solution is different from traditional, approximate solution because the number of total harmonic terms (N) is determined by the precision of harmonic amplitude quantity level, set by the investigator (e.g., AN≤ة› and ة›=108). The stability and bifurcation analysis of the period1 solutions is completed through the eigenvalue analysis of the coefficient dynamical systems of the Fourier series expressions of periodic solutions, and numerical illustrations of period1 motions are compared to verify the analytical solutions of periodic motions. The trajectories and analytical harmonic amplitude spectrum for stable and unstable periodic motions are presented. The harmonic amplitude spectrum shows the harmonic term effects on periodic motions, and one can directly know which harmonic terms contribute on periodic motions and the convergence of the Fourier series expression is clearly illustrated.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleAn Approximate Solution for Period 1 Motions in a Periodically Forced Van Der Pol Oscillator
    typeJournal Paper
    journal volume9
    journal issue3
    journal titleJournal of Computational and Nonlinear Dynamics
    identifier doi10.1115/1.4026425
    journal fristpage31001
    journal lastpage31001
    identifier eissn1555-1423
    treeJournal of Computational and Nonlinear Dynamics:;2014:;volume( 009 ):;issue: 003
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
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