Chaotic dynamics of shallow arch structures under 1:2 resonance

Journal of Engineering Mechanics

Volumn 123, Issue 6, 1997, Pages 612-619

  Malhotra, N ^a,b   Sri Namachchivaya, N ^b  

^a California Institute of Technology   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005224514     PISSN: 07339399     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-9399(1997)123:6(612)     Document Type: Article

References (25)

1. Bogoliubov, N., and Mitropolsky, Y. A. (1961). Asymptotical methods in the theory of nonlinear oscillations. Gordon and Breach, New York, N.Y.
2. Feng, Z. C., and Sethna, P. R. (1990). "Global bifurcation and chaos in parametrically forced systems with one-one resonance." Dyn. and Stability of Sys., 5, 201-225.
3. Feng, Z. C., and Sethna, P. R. (1993). "Global bifurcations in motion of parametrically excited thin plates." Nonlinear Dyn., 4, 398-408.
4. Feng, Z. C., and Wiggins, S. (1993). "On the existence of chaos in a class of two-degree-of-freedom, damped, parametrically forced mechanical systems with broken O(2) symmetry." ZAMP, 44, 201-248.
5. Hsu, C. S. (1969). "Stability of shallow arches against snap-through under time-wise step loads." AIAA J., 35(1), 31-39.
6. Huang, N. C. (1972). "Dynamic buckling of some elastic shallow structures subjected to periodic loading with high frequency." Int. J. Solids of Struct., 8, 315-326.
7. Humphrey, J. S. (1966). "On dynamic snap buckling of shallow arches." AIAA J., 4(5), 878-886.
8. Hutchinson, J. W., and Koiter, W. T. (1970). "Postbuckling theory." Appl. Mech. Rev., 23, 1353-1366.
9. Koiter, W. T. (1966). "On the nonlinear theory of thin shell structures." Proc., Koninkl. Ned. Acad. Wetenschap., B70, 1-54.
10. Kovačič, G., and Wiggins, S. (1992). "Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation." Physica D, 57, 185-225.
11. Lock, M. H. (1965). "The snapping of a shallow sinusoidal arch under a step pressure load." Tech. Rep. TRD-469 (5240-10-16), Air Force Sys. Command, Los Angeles, Calif.
12. Malhotra, N., and Sri Namachchivaya, N. (1995). "Global bifurcations in externally excited two-degrees-of-freedom nonlinear systems." Nonlinear Dyn., 8, 85-109.
13. Malhotra, N., and Sri Namachchivaya, N. (1997). "Chaotic dynamics of shallow arch structures under 1:1 resonance." J. Engrg. Mech., 123(6), 620-627.
14. Melnikov, M. H. (1963). "On the stability of the center for time periodic perturbations." Trans. Moscow Math. Soc., Moscow, Russia, 12(1), 1-57.
15. Mettler, E. (1962). Dynamic buckling. McGraw-Hill Book Co., Inc., New York, N.Y.
16. Mettler, E. (1967). "Stability and vibration problems of mechanical systems under harmonic excitation." Dynamic stability of structures, G. Hermann, ed., Pergamon Press, New York, N.Y., 169-188.
17. Plaut, R. H., and Hsieh, J. C. (1985). "Oscillations and instability of a shallow arch under two-frequency excitation." J. Sound and Vibration, 102(2), 189-201.
18. Robinson, C. (1988). "Horseshoes for autonomous Hamiltonian systems using Melnikov integral.' Ergodic Theory and Dynamical Sys., 8, 395-409.
19. Silnikov, L. P. (1965). "The case of the existence of a denumerable set of periodic motions." Soviet Math. Dokl., Moscow, Russia, 6, 163-166.
20. Sri Namachchivaya, N., and Doyle, M. M. (1988). "Chaotic motion of a shallow arch." Proc., 29th Struct., Struct. Dyn. and Mat. Conf., Am. Inst. of Aeronautics and Astronautics (AIAA), Washington, D.C., 198-209.
21. Sri Namachchivaya, N., and Malhotra, N. (1995). "Normal forms and homoclinic chaos: application to structural systems." Fields Inst. Communications, 4, 253-271.
22. Tien, W. M. (1992). "Chaotic and stochastic dynamics of structural systems," PhD thesis, Univ. of Illinois at Urbana-Champaign, Urbana, Ill.
23. Tien, W. M., Sri Namachchivaya, N., and Bajaj, A. K. (1994a). "Nonlinear dynamics of a shallow arch under periodic excitation. I: 1:2 internal resonance." Int. J. Nonlinear Mech., 29(3), 349-366.
24. Tien, W. M., Sri Namachchivaya, N., and Malhotra, N. (1994b). "Nonlinear dynamics of a shallow arch under periodic excitation. II: 1:1 internal resonance." Int. J. Nonlinear Mech., 29(3), 367-386.
25. Wiggins, S. (1988). Global bifurcations and chaos. Springer-Verlag, New York, N.Y.