Probabilistic solutions to nonlinear random ship roll motion

Journal of Engineering Mechanics

Volumn 125, Issue 5, 1999, Pages 570-574

  Er, Guo Kang ^a   lu, Vai Pan ^a  

^a UNIVERSITY OF MACAU   (Macao)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DRAG; EQUATIONS OF MOTION; FLUID STRUCTURE INTERACTION; INTEGRATION; OSCILLATIONS; POLYNOMIALS; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; WHITE NOISE;

FOKKER-PLANCK-KOLMOGOROV EQUATIONS; NONLINEAR SHIP ROLL OSCILLATIONS; NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS;

WATER WAVE EFFECTS;

PROBABILITY DENSITY FUNCTION; SHIP MOTION; WAVE;

PROBABILITY DENSITY FUNCTION; SHIP MOTION; WAVE;

EID: 0033136848     PISSN: 07339399     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-9399(1999)125:5(570)     Document Type: Article

References (18)

1. Assaf, S. A., and Zirkie, L. D. (1976). Approximate analysis of nonlinear stochastic systems. Int. J. Control, 23, 477-492.
2. Booton, R. C. (1954). Nonlinear control systems with random inputs. IRE Trans, on Circuit Tlieory, CT-l(l), 9-19.
3. Cai, G. K., and Lin, Y. K. (1988). A new approximate solution technique for randomly excited non-linear oscillators. Int. J. Non-Linear Meek, 23, 409-420.
4. Caughey, T. K. (1959). Response of a nonlinear string to random loading. J. Appl. Mech., 26(3), 341 -344.
5. Crandall, S. H. (1980). Non-Gaussian closure for random vibration of non-linear oscillators. Int. J. Non-Linear Mech., 15, 303-313.
6. Er, G. K. (1998a). Multi-Gaussian closure method for randomly excited non-linear systems. Int. J. Non-Linear Mech., 33, 201-214.
7. Er, G. K. (1998b). A new non-Gaussian closure method for the PDF solution of non-linear random vibrations. Proc., 12th Engrg. Meek Conf., ASCE, Reston, Va., 1403-1406.
8. Hampl, N. C., and Schuëller, G. I. (1989). Probability densities of the response of nonlinear substitutes under stochastic dynamic excitation. Probabilistic Engrg. Mech., England, 4, 2-9.
9. lyengar, R. N., and Dash, P. K. (1978). Study of the random vibration of nonlinear systems by the Gaussian closure technique. J. Appl. Mech., 45(2), 393-399.
10. Lutes, L. D. (1970). Approximate technique for treating random vibration of hysteretic systems. J. Acoust. Soc. Am, 48, 299-306.
11. Moshchuk, N. K., Ibrahim, R. A., and Khasminskii, R. Z. (1995a). Response statistics of ocean structures to nonlinear hydrodynamic loading. Part I: Gaussian ocean waves. J. Sound Vib., 184, 681-701.
12. Moshchuk, N. K., Ibrahim, R. A., Khasminskii, R. Z., and Chow, P. I(1995b). Asymptotic expansion of ship capsizing in random s waves-I. First-order approximation. Int. J. Non-Linear Mech., 30, 727-740.
13. Moshchuk, N. K., Ibrahim, R. A., Khasminskii, R. Z., and Chow, P. L(1995c). Asymptotic expansion of ship capsizing in random se waves-II. Second-order approximation. Int. J. Non-Linear Mech., 30,741-757.
14. Roberts, J. B. (1982). A stochastic theory for nonlinear ship rolling to irregular seas. J. Ship Res., 26, 229-245.
15. Sobczyk, K., and Trebicki, J. (1993). Maximum entropy principle nonlinear stochastic oscillators. Physica A, 193, 448-468.
16. Soong, T. T. (1973). Random differential equations in science and engineering. Academic, New York.
17. Spencer, B. F., Jr., and Bergman, L. A. (1993). On the numerical solutio of Fokker-PIanck equation for non-linear stochastic dynamics. A'linear Dyn., 4, 357-372.
18. Stratonovich, R. L. (1963). Topics in the theory of random noise, Vol. 'Gordon & Breach, New York.