Non-linear dynamics of the extended Lazer-McKenna bridge oscillation model

Dynamical Systems

Volumn 15, Issue 1, 2000, Pages 43-58

  Doole, S H ^a   Hogan, S J ^b  

^a AXA Investment Managers   (United Kingdom)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); DYNAMICS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; OSCILLATIONS; SUSPENSION BRIDGES;

LAZER-MCKENNA MODEL;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 0034156967     PISSN: 14689367     EISSN: None     Source Type: Journal    
DOI: 10.1080/026811100281929     Document Type: Article

References (14)

1. Amann, O. H., Karman, T. V., and Woodruff, G. B., 1941, The Failure of the Tacoma Narrows Bridge, Federal Works Agency.
2. Billah, K. Y., and Scanlan, R. H., 1991, Resonance, Tacoma Narrows Bridge failure, and undergraduate physics testbook. American Journal of Physics, 59: 118-124.
3. Doedel, E., Keller, H. B., and Kernevez, J. P., 1991a, Numerical analysis and control of bifurcation problems: (i) bifurcation in finite dimensions. International Journal of Bifurcation and Chaos, 1: 493-520.
4. Doedel, E., Keller, H. B., and Kernevez, J. P., 1991b, Numerical analysis and control of bifurcation problems: (i) bifurcation in finite dimensions. International Journal of Bifurcation and Chaos, 1: 745-772.
5. Doedel, E., Wang, X., and Fairgrieve, T., 1994, AUTO94: Software for continuation and bifurcation problems in ordinary differential equations. Applied Mathematics Report, California Institute of Technology, Pasadena, CA 91125.
6. Doole, S. H., and Hogan, S. J., 1996a, The nonlinear dynamics of suspension bridges under harmonic forcing. Zeitschrift für angewandte Mathematik und Mechanik, 76: (Special Issue 4): 127-128.
7. Doole, S. H., and Hogan, S. J., 1996b, A piecewise linear suspension bridge model: nonlinear dynamics and orbit continuation. Dynamics and Stability of Systems, 11: 19-47.
8. Farquharson, F. B., 1950, Aerodynamic Stability of Suspension Bridges with special reference to the Tacoma Narrows Bridge: Part I. Investigation Prior to October, 1941 (Seattle: University of Washington Press).
9. Feigin, M. I., 1970, Doubling of the oscillation period with C-bifurcations in piecewise continouous systems. PMM Journal of Mathematics and Mechanics, 34: 861-869.
10. Hogan, S. J., 1989, On the dynamics of rigid-block motion under harmonic forcing. Proceedings of the Royal Society London A, 425: 441-476.
11. Hogan, S. J., 1992, The effect of damping on rigid-block motion under harmonic forcing. Proceedings of the Royal Society London A, 437: 97-108.
12. Jacover, D., and McKenna, P. J., 1994, Nonlinear torsional flexings in a periodically forced suspended beam. Journal of Computational and Applied Mathematics, 52: 241-265.
13. Lazer, A. C., and McKenna, P. J., 1990, Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis. SIAM Review, 32: 537-578.
14. Nordmark, A. B., 1991, Non-periodic motion caused by grazing incidence in an impact oscillator. Journal of Sound Vibration, 145: 279-297.