A comment on a nonideal centrifugal vibrator machine behavior with soft and hard springs

International Journal of Bifurcation and Chaos

Volumn 16, Issue 4, 2006, Pages 1083-1088

  Dantas, Márcio José Horta ^a   Balthazar, José Manoel ^b,c  

^a FEDERAL UNIVERSITY OF UBERLÂNDIA   (Brazil)

^b SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

^c UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Center manifolds; Chaos; Hopf bifurcation; Melnikov's method; Nonideal problem

Indexed keywords

BIFURCATION (MATHEMATICS); DAMPING; MACHINE DESIGN; PARAMETER ESTIMATION; ROTATING MACHINERY; THEOREM PROVING; VIBRATORS;

CENTER MANIFOLDS; DAMPING COEFFICIENT; HOMOCLINIC CHAOS; HOPF BIFURCATION; MELNIKOV'S METHOD; NONIDEAL PROBLEMS;

CENTRIFUGES;

EID: 33745317597     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127406015349     Document Type: Review

References (9)

1. Balthazar, J. M., Mook, D. T., Weber, H. I., Brasil, R. M. L. R. F., Fenili, A., Belato, D. & Felix, J. L. P. [2003] "An overview on non-ideal vibrations," Meccanica 38, 613-621.
2. Balthazar, J. M., Brasil, R. M. L. R. F., Weber, H. I., Fenili, A., Belato, D., Felix, J. L. P. & Garzelli, F. J. A. [2004] "Review of new vibration issues due to non-ideal energy sources," in Dynamical Systems and Control, eds. Udwadia, F. E., Weber, H. I. & Leitman, G., Stability Control Theory Methods and Applications, Vol. 22 (Chapman & Hall/CRC, Boca Raton, FL), pp. 237-258.
3. Dantas, M. J. H. & Balthazar, J. M. [2003] "On the appearance of a Hopf bifurcation in a nonideal mechanical system," Mech. Res. Commun. 30, 493-503.
4. Dantas, M. J. H. & Balthazar, J. M. [2004] "On local analysis of oscillations of a non-ideal and non-ideal mechanical model," Meccanica 39, 313-330.
5. Guckenheimer, J. & Holmes, P. J. [1983] Nonlinear Oscillations, Dynamical Systems and Bifurcation's of Vector Fields (Springer-Verlag, NY).
6. Holmes, P. J. & Marsden, J. E. [1982] "Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom," Commun. Math. Phys. 82, 523-544.
7. Kononenko, V. O. [1969] Vibrating Systems with a Limited Supply Power (Illife Books Ltd., London).
8. Nayfeh, A. H. & Mook, D. T. [1979] Nonlinear Oscillations (Wiley, NY).
9. Wiggins, S. & Shaw, S. W. [1988] "Chaos and three-dimensional horseshoes in slowly varying oscillators," ASME J. Appl. Mech. 55, 959-968.