메뉴 건너뛰기




Volumn 10, Issue 2, 1996, Pages 105-133

On the local stability analysis of the approximate harmonic balance solutions

Author keywords

Bifurcations; Harmonic balance method; Linear stability analysis; Perturbation methods

Indexed keywords

APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); EQUATIONS OF MOTION; LINEARIZATION; OSCILLATORS (ELECTRONIC); PERTURBATION TECHNIQUES; STABILITY; VARIATIONAL TECHNIQUES;

EID: 0030173292     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00045453     Document Type: Article
Times cited : (17)

References (29)
  • 1
    • 0022902187 scopus 로고
    • The 1/2 subharmonic resonance and its transition to chaotic motion in a non-linear oscillator
    • Szemplińska-Stupnicka, W. and Bajkowski, J., 'The 1/2 subharmonic resonance and its transition to chaotic motion in a non-linear oscillator', International Journal of Non-Linear Mechanics 21(5), 1986, 401-429.
    • (1986) International Journal of Non-Linear Mechanics , vol.21 , Issue.5 , pp. 401-429
    • Szemplińska-Stupnicka, W.1    Bajkowski, J.2
  • 2
    • 0023288332 scopus 로고
    • Secondary resonances and approximate models of routes to chaotic motion in non-linear oscillators
    • Szemplińska-Stupnicka, W., 'Secondary resonances and approximate models of routes to chaotic motion in non-linear oscillators', Journal of Sound and Vibration 113(1), 1987, 155-172.
    • (1987) Journal of Sound and Vibration , vol.113 , Issue.1 , pp. 155-172
    • Szemplińska-Stupnicka, W.1
  • 3
    • 0343493082 scopus 로고
    • Chaotic and regular motion in non-linear systems
    • W. Szemplińska-Stupnicka, G. Iooss, and F. C. Moon (eds.), Springer-Verlag, Wien-New York
    • Szemplińska-Stupnicka, W., 'Chaotic and regular motion in non-linear systems,' in Chaotic Motions in Nonlinear Dynamical Systems, W. Szemplińska-Stupnicka, G. Iooss, and F. C. Moon (eds.), Springer-Verlag, Wien-New York, 1988, pp. 51-135.
    • (1988) Chaotic Motions in Nonlinear Dynamical Systems , pp. 51-135
    • Szemplińska-Stupnicka, W.1
  • 4
    • 0000400983 scopus 로고
    • A discussion of an analytical method of controlling chaos in Duffing's oscillator
    • Szemplińska-Stupnicka, W., 'A discussion of an analytical method of controlling chaos in Duffing's oscillator', Journal of Sound and Vibration 178(2), 1994, 276-284.
    • (1994) Journal of Sound and Vibration , vol.178 , Issue.2 , pp. 276-284
    • Szemplińska-Stupnicka, W.1
  • 16
    • 0028549241 scopus 로고
    • Use of transformations with the higher order method of multiple time scales to determine steady state periodic response of harmonically excited nonlinear oscillators. Part I: Transformation of derivative
    • Hassan, A., 'Use of transformations with the higher order method of multiple time scales to determine steady state periodic response of harmonically excited nonlinear oscillators. Part I: Transformation of derivative', Journal of Sound and Vibration 178(1), 1994, 1-19.
    • (1994) Journal of Sound and Vibration , vol.178 , Issue.1 , pp. 1-19
    • Hassan, A.1
  • 17
    • 0028550059 scopus 로고
    • Use of transformations with the higher order method of multiple time scales to determine steady state periodic response of harmonically excited nonlinear oscillators. Part II: Transformation of detuning
    • Hassan, A., 'Use of transformations with the higher order method of multiple time scales to determine steady state periodic response of harmonically excited nonlinear oscillators. Part II: Transformation of detuning', Journal of Sound and Vibration 178(1), 1994, 21-40.
    • (1994) Journal of Sound and Vibration , vol.178 , Issue.1 , pp. 21-40
    • Hassan, A.1
  • 18
    • 0039546437 scopus 로고
    • Extraneous solutions predicted by the harmonic balance method
    • Hassan, A., 'Extraneous solutions predicted by the harmonic balance method', Journal of Sound and Vibration 182(4), 1995, 523-539.
    • (1995) Journal of Sound and Vibration , vol.182 , Issue.4 , pp. 523-539
    • Hassan, A.1
  • 20
    • 0027658787 scopus 로고
    • On the steady state response and stability of nonlinear oscillators using harmonic balance
    • Hamdan, M. N. and Burton, T, D., 'On the steady state response and stability of nonlinear oscillators using harmonic balance', Journal of Sound and Vibration 166(2), 1993, 255-266.
    • (1993) Journal of Sound and Vibration , vol.166 , Issue.2 , pp. 255-266
    • Hamdan, M.N.1    Burton, T.D.2
  • 22
    • 0342781516 scopus 로고
    • Higher harmonic oscillations in heteronomous non-linear systems with one degree of freedom
    • Szemplińska-Stupnicka, W., 'Higher harmonic oscillations in heteronomous non-linear systems with one degree of freedom', International Journal of Non-Linear Mechanics 3, 1968, 17-30.
    • (1968) International Journal of Non-Linear Mechanics , vol.3 , pp. 17-30
    • Szemplińska-Stupnicka, W.1
  • 23
    • 0020101992 scopus 로고
    • A generalized Hill's method for the stability analysis of parametrically excited dynamic systems
    • Noah, S. T. and Hopkins, G. R., 'A generalized Hill's method for the stability analysis of parametrically excited dynamic systems', Journal of Applied Mechanics 49, 1982, 217-223.
    • (1982) Journal of Applied Mechanics , vol.49 , pp. 217-223
    • Noah, S.T.1    Hopkins, G.R.2
  • 26
    • 0028427256 scopus 로고
    • On the third superharmonic resonance in Duffing's oscillator
    • Hassan, A., 'On the third superharmonic resonance in Duffing's oscillator', Journal of Sound and Vibration 172(4), 1993, 513-526.
    • (1993) Journal of Sound and Vibration , vol.172 , Issue.4 , pp. 513-526
    • Hassan, A.1
  • 27
    • 0001361357 scopus 로고
    • Absence of inversion-symmetric limit cycles of even periods and the chaotic motion of Duffing's oscillator
    • Räty, R., Von Boehm, J., and Isomäki, H. M., 'Absence of inversion-symmetric limit cycles of even periods and the chaotic motion of Duffing's oscillator', Physics Letters 103A(6/7), 1984, 289-292.
    • (1984) Physics Letters , vol.103 A , Issue.6-7 , pp. 289-292
    • Räty, R.1    Von Boehm, J.2    Isomäki, H.M.3
  • 28
    • 4243654149 scopus 로고
    • Chaotic motion of a periodically driven particle in an asymmetric potential well
    • Räty, R., Von Boehm, J., and Isomäki, H. M., 'Chaotic motion of a periodically driven particle in an asymmetric potential well', Physical Review A34(5), 1986, 4310-4315.
    • (1986) Physical Review , vol.A34 , Issue.5 , pp. 4310-4315
    • Räty, R.1    Von Boehm, J.2    Isomäki, H.M.3
  • 29
    • 0024964210 scopus 로고
    • Parameter sensitivity of non-linear vibration systems
    • Peleg, K. and Hinga, S., 'Parameter sensitivity of non-linear vibration systems', Journal of Sound and Vibration 128(1), 1989, 1-11.
    • (1989) Journal of Sound and Vibration , vol.128 , Issue.1 , pp. 1-11
    • Peleg, K.1    Hinga, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.