Location of Repository

Stochastic analysis of the nonlinear response transition behavior of an ocean system



Graduation date: 2001The nonlinear response of an ocean system subjected to random excitations can exhibit very complex dynamic behaviors including jump phenomena and coexistence of attractors. In this study, the stochastic system response behavior of a simple (Duffing) oscillator under narrow-band random excitations is first examined in the subharmonic resonance region. A semi-analytical procedure based on the nonlinear response characteristics of the corresponding deterministic system is developed to derive the response transition probabilities within individual attraction domains and among finite attraction domains under the assumptions of stationarity and Markov process. Overall response amplitude probability distributions are obtained by applying the Bayes formula to the two different types of response transition probability distributions.\ud \ud To validate the prediction capability of the semi-analytical method, numerical simulation of the responses of the Duffing system are generated and statistical characteristics of the response behavior are compared with prediction results. It is shown that the semi-analytical procedure provides more accurate predictions than other approximate methods available in the literature. A parametric study on the effects of variations in excitation intensity and degree of narrow-bandedness is conducted. Results confirmed that the nonlinear response characteristics including jump phenomenon and co-existence of attraction domains are preserved under narrow-band random excitations.\ud \ud The semi-analytical prediction method developed above is then applied to analyze the stochastic response behavior of a nonlinear mooring system subjected to random ocean waves. For modeling of the structural system, a nonlinear­ structure, nonlinearly-damped (NSND) model is employed and a reverse multiple­ input/single-output technique is applied to identify the system coefficients. To verify the accuracy and capability of the semi-analytical method in predicting the complex behaviors of the nonlinear mooring system, analytical predictions are compared with experimental results and numerical simulations. System response amplitude probability distributions predicted by the semi-analytical procedure are shown to be in good agreement with experimental and simulation results

Year: 2001
OAI identifier: oai:ir.library.oregonstate.edu:1957/33222
Provided by: ScholarsArchive@OSU

Suggested articles



  1. (1993). An Introduction to Random Vibrations. Spectral & Wavelet Analysis. (3rd Ed.) Longman,
  2. (1990). Applied Probability and Stochastic Processes in Engineering and Physical Sciences. doi
  3. (1999). Experimental Analysis of a Nonlinear Moored Structure.
  4. (1993). Improved Stability Analysis of The Response of a Dulling Oscillator under Filtered White Noise. doi
  5. (1983). Introduction to Random Vibrations. doi
  6. (1992). Markov Processes. doi
  7. (2000). Noisy Nonlinear Motions of a Moored System, II: an Experimental Study, doi
  8. (1995). Noisy Nonlinear Motions of Moored Systems. Part 1: Analysis and Simulation.
  9. (1986). Nonlinear Dynamics and Chaos. doi
  10. (1987). Nonlinear Ordinary Differential Equations Second Edition. doi
  11. (1992). Nonlinear Oscillations, Bifurcations and Chaos in a Multi-Point Mooring System with a Geometric Nonlinearity doi
  12. (1979). Nonlinear Oscillations. doi
  13. (1986). Nonlinear Oscillations. Dynamical Systems and Bifurcation of Vector Fields. doi
  14. (1994). Numerical Methods for Stochastic Processes. doi
  15. (1986). Numerical Recipes: the art of scientific computing. doi
  16. (1986). On Various Definitions of the Envelope of a Random Process. doi
  17. (1971). Oscillations of a System with Nonlinear Cubic Characteristics under Narrow Band Random Excitation.
  18. (1986). Phase Plane for Narrow-Band Random Excitation of a Dulling Oscillator. doi
  19. (1992). Probabilistic Analysis of a Chaotic Dynamical System Applied Chaos,
  20. (1993). Quasi-Harmonic Analysis of the Behavior of a Hardening Dulling Oscillator Subjected to Filtered White Noise Nonlinear Dynamics,
  21. (1988). Random Superharmonic and Subharmonic esponse: Multiple Time Scaling of a Duffing Oscillator. doi
  22. (1971). Simulation of Multivariate and Multidimensional Random Processes. doi
  23. (1991). Simulation of Stochastic Processes by Spectral Representation. doi
  24. (1988). Statistical Dynamics of Nonlinear and Time-Varying Systems. doi
  25. (1998). Stochastic Analysis of Complex Nonlinear System Response Under Narrowband Excitations.
  26. (1986). Stochastic Averaging: An Approximate Method of Solving Random Vibration Problems. doi
  27. (1993). Summary and Preliminary Analysis of Nonlinear Oscillations in a Submerged Mooring System Experiment.
  28. (1990). The Response Envelope Probability Density Function of a Dulling Oscillator with Random Narrow-Band Excitation. doi
  29. (1963). Topics in the Theory of Random Noise. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.