Global optimal control and system-dependent solutions in the hardening Helmholtz-Duffing oscillator

Chaos, Solitons and Fractals

Volumn 21, Issue 5, 2004, Pages 1031-1046

  Lenci, Stefano ^a   Rega, Giuseppe ^b  

^a UNIVERSITÀ POLITECNICA DELLE MARCHE   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; COMPUTER SIMULATION; FRACTALS; HAMILTONIANS; HARDENING; HARMONIC ANALYSIS; MATHEMATICAL MODELS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION;

GLOBAL OPTIMAL CONTROL; HELMHOLTZ-DUFFING OSCILLATORS;

OSCILLATORS (MECHANICAL);

EID: 1642287596     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(03)00387-4     Document Type: Article

References (28)

1. Alaggio R, Benedettini F. The use of experimental tests in the formulation of analytical models for the finite forced dynamics of planar arches. In: Proc. DECT'01 2001 ASME Design Eng Tech Conf, Pittsburgh, Pennsylvania, USA, 9-12 September 2001 (CD ROM DETC2001/VIB21613).
2. Gjelsvik A., Bodner S.R. The energy criterion and snap buckling of arches. ASCE J. Eng. Mech. Div. (October):1962;89-134.
3. Grebogi C., Ott E., Yorke J.A. Crises, sudden changes in chaotic attractors, and transient chaos. Physica D. 7:1983;181-200.
4. Guckenheimer J., Holmes P. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. 1983;Springer-Verlag, New York.
5. Higuchi K, Dowell EH. Effect of constant transverse force on chaotic oscillations of sinusoidally excited buckled beam. In: Schiehlen W, editor. Proc. of IUTAM Symposium, Nonlinear dynamics in engineering systems. Stuttgart, Germany 21-25 August 1989. Berlin: Springer-Verlag; 1989. p. 99-106.
6. Katz A., Dowell E.H. From single well chaos to cross well chaos: a detailed explanation in terms of manifold intersections. Int. J. Bif. Chaos. 4:1994;933-941.
7. Kovacic G., Wiggins S. Orbits homoclinic to resonance, with an application to chaos in a model of the forced and damped sine-Gordon equation. Physica D. 57:1992;185-225.
8. Lenci S, Rega G. Global chaos control in a periodically forced oscillator. In: Bajaj AK, Namachchivaya NS, Franchek MA, editors. Proc ASME Int Mech Eng Congress. Nonlinear Dynamics and Control, DE-vol. 91. 17-22 Nov. 1996, Atlanta, GA. p. 111-6.
9. Lenci S., Rega G. A procedure for reducing the chaotic response region in an impact mechanical system. Nonlinear Dyn. 15:1998;391-409.
10. Lenci S., Rega G. Controlling nonlinear dynamics in a two-well impact system. Parts I and II. Int. J. Bif. Chaos. 8:1998;2387-2424.
11. Lenci S., Rega G. Optimal control of nonregular dynamics in a Duffing oscillator. Nonlinear Dyn. 33:2003;71-86.
12. Lenci S., Rega G. Optimal numerical control of single-well to cross-well chaos transition in mechanical systems. Chaos, Solitons & Fractals. 15:2003;173-186.
13. Lenci S., Rega G. Optimal control of homoclinic bifurcation: theoretical treatment and practical reduction of safe basin erosion in the Helmholtz oscillator. J. Vib. Control. 9:2003;281-316.
14. Lenci S, Rega G. A unified control framework of the nonregular dynamics of mechanical oscillators. J Sound Vibr, in press.
15. Mettler E. Dynamic buckling. Flügge W. Handbook of engineering mechanics. 1962;Mc Graw-Hill, New York.
16. Moon F.C. Chaotic and fractal dynamics. An introduction for applied scientists and engineers. 1992;Wiley, New York.
17. Moon F.C., Cusumano J., Holmes P.J. Evidence for homoclinic orbits as a precursor to chaos in a magnetic pendulum. Physica D. 24:1987;383-390.
18. Nelder J.A., Mead R. A simplex method for function minimization. Comput. J. 7:1964;308-313.
19. Pinto O.C., Gonçalves P.B. Non-linear control of buckled beams under step loading. Mech. Syst. Sign. Proc. 14:2000;967-985.
20. Shaw S.W. The suppression of chaos in periodically forced oscillators. Schiehlen W. Proc. of IUTAM Symposium, Stuttgart, Germany, 21-25 August 1989. Nonlinear Dynamics in Engineering Systems. 1989;289-296 Springer-Verlag, Berlin.
21. Szemplinska-Stupnicka W. Cross-well chaos and escape phenomena in driven oscillators. Nonlinear Dyn. 3:1992;225-243.
22. Szemplinska-Stupnicka W. The analytical predictive criteria for chaos and escape in nonlinear oscillators: a survey. Nonlinear Dyn. 7:1995;129-147.
23. Thompson J.M.T., Stewart H.B. Nonlinear dynamics and chaos. 1986;Wiley, New York.
24. Thompson J.M.T. Chaotic phenomena triggering the escape from a potential well. Proc. R. Soc. Lond. A. 421:1989;195-225.
25. Thompson J.M.T., McRobie F.A. Indeterminate bifurcations and the global dynamics of driven oscillators. Kreuzer E., Schmidt G. Proc. First Eur. Nonlinear Oscillations Conf., 16-20 August. 1993;107-128 Akademie Verlag, Hamburg, Berlin.
26. Tseng W.-Y., Dugundji J. Nonlinear vibrations of a buckled beam under harmonic excitation. ASME J. Appl. Mech. 38:1971;467-476.
27. Wiggins S. Global bifurcation and chaos: analytical methods. 1988;Springer-Verlag, New York, Heidelberg, Berlin.
28. Wiggins S. Introduction to applied nonlinear dynamical systems and chaos. 1990;Springer-Verlag, New York, Heidelberg, Berlin.