Modal interaction of resonantly forced oscillations of two-degree-of-freedom structure

Applied Mathematics and Computation

Volumn 134, Issue 2-3, 2002, Pages 217-242

  El Bassiouny, A F ^a  

^a BENHA UNIVERSITY   (Egypt)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; RESONANCE; STEEL BEAMS AND GIRDERS;

NONLINEAR MECHANICS;

OSCILLATIONS;

EID: 0037169632     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(01)00278-8     Document Type: Article

References (28)

1. Hayashi C. NonLinear Oscillation in Physical Systems. 1964;McGraw-Hill, New York.
2. Nayfeh A.H. Perturbation Methods. 1973;Wiley/Interscience, New York.
3. Evan-Iwanowski R.M. Resonance Oscillations in Mechanical System. 1976;Elsevier, New York.
4. Schmidt G., Tondal A. Nonlinear Vibrations. 1986;Cambridge University press, Cambridge.
5. Nayfeh A.H., Balachandran B. Applied Nonlinear Dynamics. 1994;Wiley/Interscience, New York.
6. Haddow G., Barr A.D.S., Mook D.T. Theoretical and experimental study of modal interaction in a two-degree-of-freedom structure. Journal of Sound and Vibrations. 97:1984;451-473.
7. Nayfeh A.H., Zavodney L.D. Experimental observation of amplitude- and phase-modulated responses of two internally coupled oscillators to harmonic excitation. Journal of Applied Mechanics. 55:1989;706-711.
8. Nayfeh A.H., Balachandran B. Experimental investigation of resonantly forced oscillations of two-degree-of-freedom strcture. International Journal of Nonlinear Mechanics. 25(2):1990;199-299.
9. Balachandran B., Colbert M.A., Nayfeh M.A. An experimental investigation of complicated response of two-degree-of-freedom structure. Journal of Applied Mechanics. 56(4):1989;960-967.
10. Goodier J.N., Mclvor I.K. The elastic cylindrical shell under nearly uniform radial impulse. Journal of Applied Mechanics. 31:1964;259-266.
11. Mclvor I.K., Lovell E.G. Dynamic response of finite-length cylindrical shells to nearly uniform radial impulse. AIAA Journal. 6:1968;2346-2351.
12. Yasuda K., Kushida G. Nonlinear forced oscillations of a shallow spherical shell. Bulletin of Japanese Society of Mechanical Engineering. 27:1984;2233-2240.
13. Nayfeh A.H., Raouf R.A. Non-linear oscillation of circular cylindrical shells. International Journal of Solids and Structures. 23:1987;1625-1638.
14. Nayfeh A.H., Raouf R.A. Non-linear forced response of circular cylindrical shells. Journal of Applied Mechanics. 54:1987;571-577.
15. Nayfeh A.H., Balachandran B. Experimental investigation of resonantly forced oscillations of two-degree-of-freedom structure. International Journal of Nonlinear Mechanics. 25(2):1990;199-209.
16. Balachandran B., Nayfeh A.H. Nonlinear oscillations of harmonically excited composite structure. Composite Structures. 16(4):1990;233-239.
17. Nayfeh A.H., Mook D.T., Sridhar S. Nonlinear analysis of the forced response of structural systems. Applied Mechanics Reviews. 42:1989;175-201.
18. Sridhar S., Nayfeh A.H., Mook D.T. Nonlinear resonances in class of multi-degree-of-freedom systems. Journal of the Acoustical Society of America. 58:1975;113-123.
19. A.H. Nayfeh, D.T. Mook, J.F. Nayfeh, Some aspects of modal interactions in the response of beams, AIAA Paper No. 87-0777 presented at the AIAA 28th Structures, Structural Dynamics and Material Conference, Monterery, CA, April 6-8, 1987.
20. Lue S.L., Cheung Y.K., Chen S. An alternative perturbation procedure of multiple scales for nonlinear dynamics systems. Journal of Applied Mechanics. 56:1989;667-675.
21. Cheung S.H.Y.K., Lue S.L. On the internal resonance of multi-degree-of-freedom systems with cubic nonlinearities. Journal of Sound and Vibration. 128:1989;13-24.
22. Nayfeh A.H., Mook D.T., Lobitz D.W. Numerical-perturbation method for the nonlinear analysis of structural vibrations. AIAA Journal. 12:1974;1222-1228.
23. Bajkowski J., Szemplinska-Stupnicka W. Internal resonance effects-simulation versus analytical method results. Journal of Sound Vibration. 104:1986;259-275.
24. Tousi S., Bajaj A.K. Period-doubling bifurcations and modulated motions in forced mechanical systems. Journal of Applied Mechanics. 52:1985;446-452.
25. Elnagger A.M., El-Bassiouny A.F. Harmonic, subharmonic, superharmonic, simulataneous sub-/superharmonic and combination resonances of self-excited two-coupled second order system to multifrequency excitations. Acta Mechanica Sicca. 8(1):1993;61-71.
26. A.M. Elnagger, A.F. El-Bassiouny, Harmonic resonance of non-linear system of rods to excitation, First International Conference of Mathematical and Physical Applications, Cairo, 1995.
27. El-Bassiouny A.F. Response of a three-degree-of-freedom system with cubic nonlinearities to harmonic excitation. Applied Mathematics and Computation. 104:1999;65-84.
28. El-Bassiouny A.F., Abdelhafez H. Predication of bifurcations for external and parametric excited one-degree-of-freedom system with quadratic, cubic and quartic nonlinearities. Mathematics and Computer in Simulation. 57:2001;61-80.