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Volumn 42, Issue 1, 2007, Pages 2-12

A novel harmonic balance analysis for the Van Der Pol oscillator

Author keywords

Chaos; Dynamical systems; Harmonic balance method; Limit cycle oscillations; Van der Pol's oscillator

Indexed keywords

CHAOS THEORY; DYNAMICAL SYSTEMS; HARMONIC ANALYSIS;

EID: 34247112827     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2006.09.004     Document Type: Article
Times cited : (46)

References (22)
  • 1
    • 29144510624 scopus 로고    scopus 로고
    • The computational efficiency of non-linear frequency domain methods
    • McMullen M.S., and Jameson A. The computational efficiency of non-linear frequency domain methods. J. Comput. Phys. 212 2 (2006) 637-661
    • (2006) J. Comput. Phys. , vol.212 , Issue.2 , pp. 637-661
    • McMullen, M.S.1    Jameson, A.2
  • 2
    • 0000855720 scopus 로고
    • A finite difference, frequency domain numerical scheme for the solution of the gust response problem
    • Scott J.R., and Atassi H.M. A finite difference, frequency domain numerical scheme for the solution of the gust response problem. J. Comput. Phys. 119 (1995) 75-93
    • (1995) J. Comput. Phys. , vol.119 , pp. 75-93
    • Scott, J.R.1    Atassi, H.M.2
  • 3
    • 0001990978 scopus 로고    scopus 로고
    • Flutter of an airfoil with a cubic nonlinear restoring force
    • Lee B.H.K., Jiang L.Y., and Wong Y.S. Flutter of an airfoil with a cubic nonlinear restoring force. J. Fluids Struct. 13 (1999) 75-101
    • (1999) J. Fluids Struct. , vol.13 , pp. 75-101
    • Lee, B.H.K.1    Jiang, L.Y.2    Wong, Y.S.3
  • 4
    • 0024281886 scopus 로고
    • On the harmonic response of an oscillator with unsymmetric restoring force
    • Virgin L.N. On the harmonic response of an oscillator with unsymmetric restoring force. J. Sound Vib. 126 1 (1988) 157-165
    • (1988) J. Sound Vib. , vol.126 , Issue.1 , pp. 157-165
    • Virgin, L.N.1
  • 5
    • 13444274398 scopus 로고    scopus 로고
    • Airfoil motion in subsonic flow with strong cubic nonlinear restoring forces
    • Lee B.H.K., Liu L., and Chung K.W. Airfoil motion in subsonic flow with strong cubic nonlinear restoring forces. J. Sound Vib. 281 3-5 (2003) 699-717
    • (2003) J. Sound Vib. , vol.281 , Issue.3-5 , pp. 699-717
    • Lee, B.H.K.1    Liu, L.2    Chung, K.W.3
  • 6
    • 18144402041 scopus 로고    scopus 로고
    • A harmonic balance approach for an airfoil with a freeplay control surface
    • Liu L., and Dowell E.H. A harmonic balance approach for an airfoil with a freeplay control surface. AIAA J. 43 4 (2005) 802-815
    • (2005) AIAA J. , vol.43 , Issue.4 , pp. 802-815
    • Liu, L.1    Dowell, E.H.2
  • 7
    • 0036531499 scopus 로고    scopus 로고
    • Nonlinear inviscid aerodynamic effects on transonic divergence, flutter, and limit-cycle oscillations
    • Thomas J.P., Dowell E.H., and Hall K.C. Nonlinear inviscid aerodynamic effects on transonic divergence, flutter, and limit-cycle oscillations. AIAA J. 40 4 (2002) 638-646
    • (2002) AIAA J. , vol.40 , Issue.4 , pp. 638-646
    • Thomas, J.P.1    Dowell, E.H.2    Hall, K.C.3
  • 8
    • 0036572063 scopus 로고    scopus 로고
    • Computation of unsteady nonlinear flows in cascades using a harmonic balance technique
    • Hall K.C., Thomas J.P., and Clark W.S. Computation of unsteady nonlinear flows in cascades using a harmonic balance technique. AIAA J. 40 5 (2002) 879-886
    • (2002) AIAA J. , vol.40 , Issue.5 , pp. 879-886
    • Hall, K.C.1    Thomas, J.P.2    Clark, W.S.3
  • 9
    • 33645885601 scopus 로고    scopus 로고
    • A comparison of two harmonic balance approaches for Duffing's oscillators: classical and high dimensional
    • Liu L., Thomas J.P., Dowell E.H., Attar P., and Hall K.C. A comparison of two harmonic balance approaches for Duffing's oscillators: classical and high dimensional. J. Comput. Phys. 215 1 (2006) 298-320
    • (2006) J. Comput. Phys. , vol.215 , Issue.1 , pp. 298-320
    • Liu, L.1    Thomas, J.P.2    Dowell, E.H.3    Attar, P.4    Hall, K.C.5
  • 10
    • 34047163427 scopus 로고    scopus 로고
    • L. Liu, E.H. Dowell, J.P. Thomas, Higher order harmonic balance analyis for limit cycle oscillations in an airfoil with cubic restoring forces, J. Fluids Struct. 23 (3) (2007) in press.
  • 11
    • 0000873906 scopus 로고
    • On relaxation-oscillations
    • Van Der Pol B. On relaxation-oscillations. Phil. Mag. Ser. 7 2 (1926) 978-992
    • (1926) Phil. Mag. Ser. , vol.7 , Issue.2 , pp. 978-992
    • Van Der Pol, B.1
  • 15
    • 0000585613 scopus 로고
    • Asymptotic solution of van der Pol's equation
    • (in Russian), Amer. Math. Soc. Transl. 88 (1953) (English Translation)
    • Dorodnicyn A.A. Asymptotic solution of van der Pol's equation. Prikl. Mat. Mekh. 11 (1947) 313-328 (in Russian), Amer. Math. Soc. Transl. 88 (1953) (English Translation)
    • (1947) Prikl. Mat. Mekh. , vol.11 , pp. 313-328
    • Dorodnicyn, A.A.1
  • 17
    • 0043040918 scopus 로고    scopus 로고
    • On the route to strangeness without chaos in the quasiperiodically forced van der Pol oscillator
    • Pokorn P., Schreiber I., and Marek M. On the route to strangeness without chaos in the quasiperiodically forced van der Pol oscillator. Chaos, Solitons and Fractals 7 3 (1996) 409-424
    • (1996) Chaos, Solitons and Fractals , vol.7 , Issue.3 , pp. 409-424
    • Pokorn, P.1    Schreiber, I.2    Marek, M.3
  • 18
    • 0003066387 scopus 로고    scopus 로고
    • The global bifurcation characteristics of the forced van der Pol oscillator
    • Xu J.X., and Jiang J. The global bifurcation characteristics of the forced van der Pol oscillator. Chaos, Solitons and Fractals 7 1 (1996) 3-19
    • (1996) Chaos, Solitons and Fractals , vol.7 , Issue.1 , pp. 3-19
    • Xu, J.X.1    Jiang, J.2
  • 19
    • 0030647521 scopus 로고    scopus 로고
    • The coexistence of periodic, almost periodic and chaotic attractors in the Van Der Pol-Duffing oscillator
    • Szempliska-Stupnicka W., and Rudowski J. The coexistence of periodic, almost periodic and chaotic attractors in the Van Der Pol-Duffing oscillator. J. Sound Vib. 199 2 (1997) 165-175
    • (1997) J. Sound Vib. , vol.199 , Issue.2 , pp. 165-175
    • Szempliska-Stupnicka, W.1    Rudowski, J.2
  • 20
    • 3042521066 scopus 로고    scopus 로고
    • A method to determine the periodic solution of the non-linear dynamics system
    • Dexin Li, and Jianxue Xu. A method to determine the periodic solution of the non-linear dynamics system. J. Sound Vib. 275 1-2 (2004) 1-16
    • (2004) J. Sound Vib. , vol.275 , Issue.1-2 , pp. 1-16
    • Dexin Li1    Jianxue Xu2
  • 21
    • 0032153758 scopus 로고    scopus 로고
    • The periodic solution of Van Der Pol's equation
    • Buonomo A. The periodic solution of Van Der Pol's equation. SIAM J. Appl. Math. 59 1 (1998) 156-171
    • (1998) SIAM J. Appl. Math. , vol.59 , Issue.1 , pp. 156-171
    • Buonomo, A.1
  • 22
    • 0141555777 scopus 로고
    • Relaxation oscillations governed by a Van der Pol equation with periodic forcing term
    • Grasman J., Veling E.J.M., and Willems G.M. Relaxation oscillations governed by a Van der Pol equation with periodic forcing term. SIAM J. Appl. Math. 31 (1976) 667-676
    • (1976) SIAM J. Appl. Math. , vol.31 , pp. 667-676
    • Grasman, J.1    Veling, E.J.M.2    Willems, G.M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.