Bifurcations and chaos of an immersed cantilever beam in a fluid and carrying an intermediate mass

Journal of Sound and Vibration

Volumn 253, Issue 4, 2003, Pages 859-888

  Al Qaisia, A A ^a   Hamdan, M N ^b  

^a UNIVERSITY OF JORDAN   (Jordan)

^b KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; COMPUTER SIMULATION; DAMPING; FLUIDS; HARMONIC ANALYSIS; LINEAR EQUATIONS; RESONANCE; SYSTEM STABILITY; VIBRATIONS (MECHANICAL);

IMMERSED CANTILEVER BEAM; NON-LINEAR DYNAMIC MODEL; PERIOD-DOUBLING BIFURCATION CRITERION; TWO-TERM HARMONIC BALANCE METHOD;

CANTILEVER BEAMS;

EID: 0037435456     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.2001.4072     Document Type: Article

References (32)

1. A. Nayfeh 2000 Nonlinear Interaction: Analytical, Computational and Experimental Methods. New York: John Wiley & Sons.
2. W. Szemplinska-Stupnicka 1986 International Journal of Nonlinear Mechanics 23, 257-277. Bifurcations of harmonic solution leading to chaotic motion in the softening type Duffing's oscillator.
3. W. Szemplinska-Stupnicka 1987 Journal of Sound and Vibration 113, 155-172. Secondary resonance and approximate models of rout to chaotic motion in non-linear oscillators.
4. W. Szemplinska-Stupnicka and J. Bajkowski 1986 International Journal of Non-Linear Mechanics 21, 401-419. The 1/2 subharmonic resonance and its transition to chaotic motion in a non-linear oscillator.
5. J. C. Huang, Y. H. Kao, C. S. Wang and Y. Gou 1989 Physics Letters A 136, 131-138. Bifurcation structure of the Duffing oscillator with asymmetric potential well.
6. K. L. Liu and K. Young 1986 Journal of Mathematics and Physics 27, 502-506. Stability of forced nonlinear oscillators via Poincaré map.
7. Jherath and K. Fesser 1987 Physical Letters A 120, 265-268. Mode expansions and bifurcations in nonlinear single-well oscillators.
8. A. H. Nayfeh and N. E. Sanchez 1989 International Journal of Non-linear Mechanics 24, 483-497. Bifurcations in a forced softening Duffing oscillator.
9. Z. Rahman and T. D. Burton 1986 Journal of Sound and Vibration 110, 363-380. Large amplitude primary superharmonic resonances in the Duffing oscillator.
10. W. Szemplinska-Stupnika 1994 Journal of Sound and Vibration 178, 276-284. A discussion of an analytical method of controlling chaos in Duffing oscillator.
11. A. Hassan 1994 Journal of Sound and Vibration 172, 513-526. On the third superharmonic resonance in the Duffing oscillator.
12. B. A. Huberman and J. P. Crutchfield 1979 Physica Review Letters 43, 1743-1747. Chaotic states of anharmonic systems in periodic fields.
13. R. Raty, J. Von Boehm and H. M. Isomaki 1984 Physical Letters A 103, 289-292. Absence of inversion-symmetric limit cycles of even periods and chaotic motion on Duffing oscillator.
14. R. Van Dooren 1988 Journal of Sound and Vibration 23, 327-339. On the transition from regular to chaotic behavior in the Duffing oscillator.
15. M. N. Hamdan and T. D. Burton 1993 Journal of Sound and Vibration 166, 255-266. On the steady state response and stability of non-linear oscillators using harmonic balance.
16. K. R. Asfar and K. K. Masoud 1992 Journal of Vibration and Acoustics 144, 489-494. On the period-doubling bifurcations in the Duffing's oscillator with negative linear stiffness.
17. J. Awrejcewicz and J. Mrozowski 1989 Journal of Sound and Vibration 89, 89-100. Bifurcation and chaos of a particular Van Der Pol-Duffing oscillator.
18. L. D. Zavodney, A. H. Nayfeh and N. E. Sanchez 1989 Journal of Sound and Vibration 129, 417-442. The response of a single-degree-of-freedom system with quadratic and cubic non-linearities to a principal parametric resonance.
19. A. Hassan 1996 Nonlinear Dynamics 10, 105-133. On the local stability analysis of the approximate harmonic balance solutions.
20. A. A. Al-Qaisia and M. N. Hamdan 2001 Journal of Sound and Vibration 244, 453-479. Bifurcation of approximate harmonic balance solution and transition to chaos in an oscillator with inertial and elastic symmetric nonlinearities.
21. A. A. Al-Qaisia, B. O. Al-Bedoor and M. N. Hamdan 2000 Shock and Vibration 7, 179-194. On the steady state response of a cantilever beam partially immersed in a fluid and carrying an intermediate mass.
22. L. D. Zavodney and A. H. Nayfeh 1989 International Journal of Nonlinear Mechanics 24, 105-125. The nonlinear response of a slender beam carrying a lumped mass to a principal parametric excitation: theory and experiment.
23. M. R. M. Crespo Da Silva and C. C. Glynn 1978 Journal of Structural Mechanics 6, 437-448. Nonlinear flexural-flexural-torsional dynamics of inextensible beams, I: equations of motion.
24. M. N. Hamdan and N. H. Shabaneh 1997 Journal of Sound and Vibration 199, 737-750. On the period of large amplitude free vibrations of conservative autonomous oscillators with static and inertia nonlinearities.
25. H. N. Arafat, A. H. Nayfeh and C. Chin 1998 Nonlinear Dynamics 15, 31-61. Nonlinear nonplanar dynamics of parametrically excited cantilever beams.
26. J. Y. Chang and W. H. Liu 1989 Journal of Sound and Vibration 130, 516-524 Some studies on the natural frequencies of immersed restrained column
27. A. A. Al-Qaisia and M. N. Hamdan 1999 Journal of Sound and Vibration 223, 49-71. On the steady state response of oscillators with static and inertia non-linearities.
28. A. Wolf, J. B. Swift, H. L. Swinney and J. A. Vastano 1985 Physica D 16, 285-317. Determining Lyapunov exponent from a time series.
29. F. C. Moon 1987 Chaotic Vibrations. New York: John Wiley & Sons.
30. T. D. Burton 1994 Introduction to Dynamic Systems Analysis. New York: McGraw-Hill
31. B. O. Al-Bedoor and Y. Khulief 1997 Journal of Sound and Vibration 206, 641-661. General planar dynamics of a sliding flexible link.
32. S. W. Shaw 1988 Journal of Sound and Vibration 124, 329-343. Chaotic dynamics of a slender beam rotating about its longitudinal axis.