Deterministic and stochastic analyses of chaotic and overturning responses of a slender rocking object

Nonlinear Dynamics

Volumn 11, Issue 1, 1996, Pages 83-106

  Lin, H ^a   Yim, S C S ^a  

^a Oregon State University   (United States)

Author keywords

Chaotic; Deterministic; Foguel alternative theorem; Fokker Planck equation; Generalized stochastic Melnikov process; Invariant manifolds; Mean Poincar map; Overturning; Probability density function (PDF); Slender rocking object; Stochastic

Indexed keywords

CHAOS THEORY; DYNAMICS; FUNCTIONS; NUMERICAL ANALYSIS; NUMERICAL METHODS; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES;

FOGUEL ALTERNATIVE THEOREM; MELNIKOV FUNCTION; PERIODIC EXCITATION; POINCARE SECTION; RANDOM NOISE; SLENDER ROCKING OBJECT; STOCHASTIC EXTENSION;

DYNAMIC RESPONSE;

EID: 0030230450     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00045052     Document Type: Article

References (26)

1. Aslam, M., Godden, W. G., and Scalise, D. T., 'Earthquake rocking response of rigid bodies', Journal of Structural Engineering Division, ASCE 106, 1980, 377-392.
2. Yim, S. C. S., Chopra, A. K., and Penzien, J., 'Rocking response of rigid blocks to earthquakes', Earthquake Engineering and Structural Dynamics 8, 1980, 565-587.
3. Spanos, P. D. and Koh, A. S., 'Rocking of rigid blocks due to harmonic shaking', Journal of Engineering Mechanics Division, ASCE 110, 1984, 1627-1642.
4. Wong, C. M. and Tso, W. K., 'Steady state rocking response of rigid blocks, Part II: Experiment', Earthquake Engineering and Structural Dynamics 18, 1989, 107-120.
5. Hogan, S. J., 'On the dynamics of rigid-block motion under harmonic forcing', Proceedings of Royal Society of London A 425, 1989, 441-476.
6. Yim, S. C. S. and Lin, H., 'Nonlinear impact and chaotic response of slender rocking objects', Journal of Engineering Mechanics Division, ASCE 117, 1991, 2079-2100.
7. Yim, S. C. S. and Lin, H., 'Chaotic behavior and stability of free-standing offshore equipment', Ocean Engineering 18, 1991, 225-250.
8. Yim, S. C. S. and Lin, H., 'Probabilistic analysis of a chaotic dynamical system', in Applied Chaos, J. H. Kim and J. Stringer (eds.), John Wiley & Sons, New York, 1992, pp. 219-241.
9. Koh, A. S., 'Rocking of rigid blocks on randomly shaking foundations', Nuclear Engineering and Design 97,1986, 269-276.
10. Iyengar, R. N. and Manohar, C. S., 'Rocking response of rectangular rigid blocks under random noise base excitations ', International Journal of Non-Linear Mechanics 26, 1991, 885-892.
11. Dimentberg, M. F., Lin, Y. K., and Zhang, R., Toppling of computer-type equipment under base excitation', Journal of Engineering Mechanics Division, ASCE 119, 1993, 145-160.
12. Bruhn, B. and Koch, B. P., 'Heteroclinic bifurcations and invariant manifolds in rocking block dynamics', Zeitschrift für Naturforschung 46a, 1991, 481-490.
13. Lin, H. and Yim, S. C. S., 'Nonlinear rocking motions, II: Overturning under random excitations', to appear in Journal of Engineering Mechanics Division, ASCE.
14. Kapitaniak, T., Chaos in Systems with Noise, World Scientific, Singapore, 1988.
15. Risken, H., The Fokker-Planck Equation: Methods of Solution and Applications, Springer-Verlag, Berlin/Heidelberg, 1984.
16. Wu, Y. J., Yim, S. C. S., and Lin, H., 'Stochastic response of chaotic systems to combined periodic and random excitations', Report No. OE-95-05, Oregon State University, Ocean Engineering Program, 1995.
17. Guckenheimer, J. and Holmes P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983.
18. Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, 1990.
19. Jordan, D. W. and Smith, P., Nonlinear Ordinary Differential Equations, Oxford University Press, Oxford, 1987.
20. Parker, T. S. and Chua, L. O., Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, New York, 1989.
21. Haken, H., 'Generalized Onsager-Machlup function and classes of path integral solutions of the Fokker-Planck equation and the Master equations', Zeitschrift für Physik B 24, 1976, 321-326.
22. Wehner, M. F. and Wolfer, W. G ., 'Numerical evaluation of path-integral solutions to Fokker-Planck equations', Physical Review A 27, 1983, 2663-2670.
23. Shinozuka, M., 'Simulation of multivariate and multidimensional random processes', Journal of Acoustical Society of America 49, 1977, 357-367.
24. Thompson, J. M. T. and Stewart, H. B., Nonlinear Dynamics and Chaos, John Wiley & Sons, Chichester, 1986.
25. Lasota, A. and Mackey, M. C., Chaos, Fractals, and Noise, 2nd Ed., Springer-Verlag, New York, 1994.
26. Falzarano, J., Shaw, S. W., and Troesch, A. W., 'Application of global methods for analyzing dynamical systems to ship rolling motion and capsizing', International Journal of Bifurcation and Chaos 2, 1992, 101-115.