Multiple time scale analysis for bifurcation from a double-zero eigenvalue

Proceedings of the ASME Design Engineering Technical Conference

Volumn 7B-1999, Issue , 1999, Pages 1659-1666

  Luongo, Angelo ^a   Paolone, Achille ^a   Egidio, Angelo Di ^a  

^a UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); DYNAMICAL SYSTEMS; JACOBIAN MATRICES; VIBRATIONS (MECHANICAL);

BIFURCATION EQUATIONS; CENTER MANIFOLD; FRACTIONAL POWER; MECHANICAL BEHAVIOR; MULTIPLE SCALE METHOD; MULTIPLE TIME SCALE; NORMAL FORM METHODS; PERTURBATION PARAMETERS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 85039665479     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC99-VIB-8053     Document Type: Conference Paper

References (13)

1. Nayfeh, A.H., and Mook, D.T., Nonlinear Oscillations, Wiley, New York, 1979.
2. Luongo, A., and Paolone, A., 'On the Reconstitution Problem in the Multiple Time Scale Method', Nonlinear Dynamics, 1999, in press.
3. Luongo, A., and Paolone, A., 'Perturbation methods for bifurcation analysis from multiple nonresonant complex eigenvalues', Nonlinear Dynamics 14, 1997, 193-210.
4. Luongo, A., and Paolone, A., 'Multiple Scale Analysis for Divergence-Hopf Bifurcation of Imperfect Symmetric Systems,' Journal of Sound and Vibration, 1999.
5. Luongo, A., 'Eigensolutions Sensitivity for Nonsymmetric Matrices with Repeated Eigenvalues', AIAA Journal, 31, 1993, 1321-1328.
6. Luongo, A., Paolone, A., and Di Egidio, A., 'Sensitivities and Linear Stability Analysis Around a Double Zero Eigenvalue'. Submitted to AIAA Journal.
7. Wilkinson, J.H., The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, England, UK, 1965.
8. Maslowe, S.A., 'Direct resonance in double-diffusive systems', Studies in Applied Mathematics 73, 1985, 59-74.
9. Moroz, I.M., 'Amplitude expansion and normal forms in a model for thermohaline convection', Studies in Applied Mathematics 74, 1986, 155-170.
10. Nayfeh, A.H., 'Topical course on nonlinear dynamics', Societa Italiana di Fisica, Santa Margherita di Pula, Sardinia, Perturbation Methods in Nonlinear Dynamics, 1985.
11. Guckenheimer, J., and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983.
12. Iooss, G, and Joseph, D.D., Elementary Stability and Bifurcation Theory, Springer-Verlag, New York, 1980.
13. Troger, H., and Steindl, A., Nonlinear Stability and Bifurcation Theory, Springer Verlag, Wien, New York, 1991.