The probabilistic solutions tononlinear random vibrationsof Multi-Degree-Of-Freedom systems

Journal of Applied Mechanics, Transactions ASME

Volumn 67, Issue 2, 2000, Pages 355-359

  Er, G K ^a  

^a UNIVERSITY OF MACAU   (Macao)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; INTEGRATION; MONTE CARLO METHODS; NONLINEAR EQUATIONS; NONLINEAR SYSTEMS; POLYNOMIALS; PROBABILITY DENSITY FUNCTION; VIBRATIONS (MECHANICAL);

FOKKER-PLANK-KOLMOGOROV EQUATION; NONLINEAR RANDOM VIBRATIONS; QUADRATIC ALGEBRAIC EQUATIONS;

DEGREES OF FREEDOM (MECHANICS);

EID: 0034204716     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.1304842     Document Type: Article

References (15)

1. Booton, R. C., 1954, “Nonlinear Control Systems With Random Inputs,” IRE Trans. Circuit Theory, CT-1, 1, pp. 9-19.
2. Caughey, T. K., 1959, “Response of a Nonlinear String to Random Loading,” ASME J. Appl. Mech., 26, pp. 341-344.
3. Lin, Y. K., 1967, Probabilistic Theory of Structure Dynamics, McGraw-Hill, New York.
4. Iwan, W. D., 1973, “A Generalization of the Concept of Equivalent Linearization,” Int. J. Non-Linear Mech., 5, pp. 279-287.
5. Assaf, S. A., and Zirkie, L. D., 1976, “Approximate Analysis of Nonlinear Stochastic Systems,” Int. J. Control, 23, pp. 477-492.
6. Soize, C., 1988, “Steady-State Solution of Fokker-Planck Equation in Higher Dimension,” Prob. Eng. Mech., 3, pp. 196-206.
7. Stratonovich, R. L., 1963, Topics in the Theory of Random Noise, Vol. 1, Gordon and Breach, New York.
8. Sobczyk, K., and Trebicki, J., 1990, “Maximum Entropy Principle in Stochastic Dynamics,” Prob. Eng. Mech., 5, pp. 102-110.
9. Er, G. K., 1998, “Multi-Gaussian Closure Method for Randomly Excited Nonlinear Systems,” Int. J. Non-Linear Mech., 33, pp. 201-214.
10. Shinozuka, M., 1972, “Monte Carlo Simulation of Structural Dynamics,” Comput. Struct., 2, pp. 855-874.
11. Harris, C. J., 1979, “Simulation of Multivariate Nonlinear Stochastic System,” Int. J. Numer. Methods Eng., 14, pp. 37-50.
12. Kloeden, P. E., and Platen, E., 1995, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin.
13. Er, G. K., 1999, “A Consistent Method for the PDF Solutions of Random Oscillators,” ASCE Journal of Engineering Mechanics, 125, pp. 443-447.
14. Soong, T. T., 1973, Random Differential Equations in Science and Engineering, Academic Press, New York.
15. Scheurkogel, A, and Elishakoff, I, 1988, “Non-linear Random Vibration of a Two-Degree-of-Freedom System,” Non-Linear Stochastic Engineering Systems, F. Ziegler and G. I. Schueller, eds., Springer-Verlag, Berlin, pp. 285-299.