Effect of fast harmonic excitation on frequency-locking in a van der Pol-Mathieu-Duffing oscillator

Communications in Nonlinear Science and Numerical Simulation

Volumn 14, Issue 1, 2009, Pages 244-253

  Fahsi, Abdelhak ^a   Belhaq, Mohamed ^b  

^a HASSAN II UNIVERSITY OF CASABLANCA   (Morocco)

^b HASSAN II UNIVERSITY   (Morocco)

Author keywords

Fast excitation; Frequency locking; Parametric forcing; Self excitation

Indexed keywords

FREQUENCY RESPONSE; HARMONIC ANALYSIS; LOCKS (FASTENERS); OSCILLATORS (MECHANICAL);

FAST EXCITATION; FREQUENCY LOCKING; HARMONIC EXCITATION; MAIN RESONANCE; MATHIEU-DUFFING OSCILLATOR; PARAMETRIC FORCING; SELF EXCITATION; SLOW DYNAMICS; SLOW FLOW; VAN DER POL;

MODULATION;

EID: 45249116981     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2007.07.010     Document Type: Article

References (27)

1. Tondl A. On the interaction between self-excited and parametric vibrations. National Research Institute for Machine Design, Monographs and Memoranda No. 25, Prague; 1978.
2. Schmidt G. Interaction of self-excited forced and parametrically excited vibrations. The 9th international conference on nonlinear oscillations. Application of the theory of nonlinear oscillations vol. 3 (1984), Naukowa Dumka, Kiev
3. Szabelski K., and Warminski J. Self-excited system vibrations with parametric and external excitations. J Sound Vib 187 4 (1995) 595-607
4. Szabelski K., and Warminski J. The nonlinear vibrations of parametrically self-excited system with two degrees of freedom under external excitation. Nonlinear Dynam 14 (1997) 23-36
5. Belhaq M., Clerc R.L., and Hartman C. Etude numérique d'une 4-résonance d'une équation de Liénard forcée. CR Acad Sci Paris 303 II-10 (1986) 873-876
6. Belhaq M. Numerical study for parametric excitation of differential equation near a 4-resonance. Mech Res Commun 17 4 (1990) 199-206
7. Belhaq M., and Fahsi A. Higher-order approximation of subharmonics close to strong resonances in the forced oscillators. Comput Math Appl 33 8 (1997) 133-144
8. Yano S. Analytic research on dynamic phenomena of parametrically and self-exited mechanical systems. Ing Arch 57 (1987) 51-60
9. Yano S. Considerations on self- and parametrically excited vibrational systems. Ing Arch 59 (1989) 285-295
10. Abouhazim N., Belhaq M., and Lakrad F. Three-period quasi-periodic solutions in self-excited quasi-periodic Mathieu oscillator. Nonlinear Dynam 39 (2005) 395-409
11. Pandey M., Rand R.H., and Zehnder A. Frequency locking in a forced Mathieu-van der Pol-Duffing system. Nonlinear Dynam (2007) 10.1007/s11071-007-9238-x
12. Pandey M., Rand R.H., and Zehnder A. Perturbation analysis of entrainment in a micromechanical limit cycle oscillator. Commun Nonlinear Sci Numer Simul 12 (2007) 1291-1301
13. Chelomei V.N. Mechanical paradoxes caused by vibrations. Soviet Phys Dokl 28 (1983) 387-390
14. Tcherniak D. The influence of fast excitation on a continuous system. J Sound Vib 227 2 (1999) 343-360
15. Thomsen J.J. Some general effects of strong high-frequency excitation: stiffening, biasing, and smoothening. J Sound Vib 253 4 (2002) 807-831
16. Jensen J.S., Tcherniak D.M., and Thomsen J.J. Stiffening effects of high-frequency excitation: experiments for an axially loaded beam. J Appl Mech 67 2 (2000) 397-402
17. Hansen M.H. Effect of high-frequency excitation on natural frequencies of spinning discs. J Sound Vib 234 4 (2000) 577-589
18. Chatterjee S., Singha T.K., and Karmakar S.K. Non-trivial effect of fast vibration on the dynamics of a class of nonlinearly damped mechanical systems. J Sound Vib 260 4 (2003) 711-730
19. Thomsen J.J. Using fast vibrations to quench friction-induced oscillations. J Sound Vib 228 5 (1999) 1079-1102
20. Mann B.P., and Koplow M.A. Symmetry breaking bifurcations of a parametrically excited pendulum. Nonlinear Dynam 46 (2006) 427-437
21. Sah S.M., and Belhaq M. Effect of vertical high-frequency parametric excitation on self-excited motion in a delayed van der Pol oscillator. Chaos Soliton Fract (2006) 10.1016/j.chaos.2006.10.040
22. Belhaq M., and Sah S.M. Horizontal fast excitation in delayed van der Pol oscillator. Commun Nonlinear Sci Numer Simul (2007) 10.1016/j.cnsns.2007.02.007
23. Blekhman I.I. Vibrational mechanics - nonlinear dynamic effects, general approach, application (2000), World Scientific, Singapore
24. Belhaq M., and Houssni M. Quasi-periodic oscillations, chaos and suppression of chaos in a nonlinear oscillator driven by parametric and external excitations. Nonlinear Dynam 18 (1999) 1-24
25. Rand R.H., Guennoun K., and Belhaq M. 2:2:1 Resonance in the quasi-periodic Mathieu equation. Nonlinear Dynam 31 (2003) 187-193
26. Abouhazim N., Rand R.H., and Belhaq M. The damped nonlinear quasi-periodic Mathieu equation near 2:2:1 resonance. Nonlinear Dynam 45 (2006) 237-247
27. Nayfeh A.H., and Mook D.T. Nonlinear oscillations (1979), Wiley, New York