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Van der Pol方程极限环的摄动—迭代解法 被引量:1

PEPTURBATIONITERATIVE METHOD FOR LIMIT CYCLES OF THE VAN DER POL EQUATION
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摘要 本文应用摄动—迭代解法研究VanderPol方程,可以依据定的精确度求出极限环的方程,与数值积分法作了比较。 This paper investigates the limit cycles of the Van der Pol equation by using the perturbationiterative method. Thei lmit cycles can be calculated to any desired degress of accuracy. A comparison with the numerically calculated result shows that perturbationiterative method has its advantage.
作者 林洁贤
出处 《华南师范大学学报(自然科学版)》 CAS 1997年第2期81-84,共4页 Journal of South China Normal University(Natural Science Edition)
关键词 POL方程 极限环 摄动-迭代法 Van der Pol equation limit cycls perturbationiterative method
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  • 1刘菲,杨翊仁.立方非线性机翼的二重半稳定极限环分叉[J].西南交通大学学报,2004,39(5):638-640. 被引量:5
  • 2张琪昌,刘海英,任爱娣.具有立方非线性机翼颤振的局部分岔[J].天津大学学报(自然科学与工程技术版),2004,37(11):970-974. 被引量:9
  • 3WANG C C,CHEN C L, YAU H T. Bifurcation and cha-otic analysis of aeroelastic systems [ J ]. Journal of Compu-tational and Nonlinear Dyamics, 2014, 10 ( 9 ) : Art021004,13pp.
  • 4CHEN Y M,LIU J K. Nonlinear aeroelastic analysis of anairfoil-store system with a freeplay by precise integrationmethod [ J ]. Journal of Fluids and Structures, 2014, 46(4): 149-164.
  • 5DAI H H,YUE X K,LIU C S. A multiple scale time do-main collocation method for solving non-linear dynamicalsystem [ J ]. International Journal of Non-linear Mechanics,2014, 67(6): 342-351.
  • 6CHUNG K W,HE Y B, LEE B H K. Bifurcation analysisof a two-degree-of-freedom aeroelastic system with hyste-resis structural nonlinearity by a perturbation-incrementalme-thod[ J]. Journal of Sound and Vibration, 2009, 320(3): 163-183.
  • 7MURUA J, PALACIOS R,GRAHAM J M R. Assessmentof wake-tail interference effects on the dynamics of flexi-ble aircraft [ J ] . AIAA Journal, 2012, 50(7): 1575 -1585.
  • 8LEE B H K,PRICE S J,WONG Y S. Nonlinear aero-elastic analysis of airfoils : bifurcation and chaos[ J]. Pro-gress Aerospace Science, 1999, 35(3) : 205-344.
  • 9LIU L P,DOWELL E H. The secondary bifurcation of anaeroelastic airfoil motion : effect of high harmonics [ J ].Nonlinear Dynamics, 2004,37(3) : 31-49.
  • 10LEE B H K,LIU L,CHUNG K W. Airfoil motion in sub-sonic flow with strong cubic nonlinear restoring forces [ J ].Journal of Sound and Vibration, 2005,281 ( 2) : 699-717.

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