Chaotic motion of shallow arch structures under 1:1 internal resonance

Journal of Engineering Mechanics

Volumn 123, Issue 6, 1997, Pages 620-627

  Malhotra, N ^a   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: 0000699143     PISSN: 07339399     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-9399(1997)123:6(620)     Document Type: Article

References (12)

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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. 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.
6. Malhotra, N., and Sri Namachchivaya, N. (1995). "Global bifurcations in externally excited two-degrees-of-freedom nonlinear systems." Nonlinear Dyn., 8, 85-109.
7. Malhotra, N., and Sri Namachchivaya, N. (1997). "Chaotic dynamics of shallow arch structures under 1:2 internal resonance." J. Engrg. Mech., 123(6), 612-619.
8. Melnikov, M. H. (1963). "On the stability of the center for time periodic perturbations." Trans. Moscow Math. Soc., Moscow, 12(1), 1-57.
9. Robinson, C. (1988). "Horseshoes for autonomous Hamiltonian systems using Melnikov integral." Ergodic Theory and Dynamical Sys., 8, 395-409.
10. Silnikov, L. P. (1965). "The case of the existence of a denumerable set of periodic motions." Soviet Math. Dokl., Moscow, Russia, 6, 163-166.
11. Tien, W. M., Sri Namachchivaya, N., and Malhotra, N. (1994). "Nonlinear dynamics of a shallow arch under periodic excitation. II: 1:1 internal resonance." Int. J. Nonlinear Mech., 29(3), 367-386.
12. Wiggins, S. (1988). Global bifurcations and chaos. Springer-Verlag, New York, N.Y.