Stationary and non-stationary probability density function for non-linear oscillators

International Journal of Non-Linear Mechanics

Volumn 32, Issue 6, 1997, Pages 1051-1064

  Muscolino, G ^a   Ricciardi, G ^a   Vasta, M ^b  

^a UNIVERSITY OF MESSINA   (Italy)

^b UNIVERSITY OF PALERMO   (Italy)

Author keywords

Gram Charlier expansions; Probability density function; Stochastic non linear dynamics

Indexed keywords

DIFFERENTIAL EQUATIONS; FREQUENCY RESPONSE; NONLINEAR EQUATIONS; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES;

C TYPE GRAM CHARLIER SERIES EXPANSION; FOKKER PLANCK EQUATION; NONLINEAR OSCILLATORS; NONSTATIONARY PROBABILITY DENSITY FUNCTION; STATIONARY PROBABILITY DENSITY FUNCTION; STOCHASTIC NONLINEAR DYNAMICS; WEIGHTED RESIDUAL METHOD;

OSCILLATORS (MECHANICAL);

EID: 0031273409     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0020-7462(96)00134-5     Document Type: Article

References (13)

1. J. B. Roberts and P. D. Spanos, Random Vibration and Statistical Linearization. Wiley, New York (1990).
2. T. K. Caughey, On the response of non-linear oscillator to stochastic excitation. Prob. Engng Mech. 1, 2-4 (1986).
3. G. Muscolino, Response of linear and non-linear structural systems under Gaussian and non-Gaussian filtered input. Dynamic Motion Chaotic and Stochastic Behaviour. CISM Course and Lectures No. 340 (Edited by F. Casciati), pp. 203-301. Springer-Verlag (1993).
4. R. L. Stratonovich, Topics in the Theory of Random Noise, Vol. 1. Gordon & Breach, New York (1967).
5. Y. Yong and Y. K. Lin, Exact stationary response solution for second order non-linear systems under parametric and external white noise excitations. J. Appl. Mech. ASME 54, 414-418 (1987).
6. G. Q. Cai and Y. K. Lin, Exact stationary response solution for second order non-linear systems under parametric and external white noise excitations - Part II. J. Appl. Mech. ASME 23, 315-325 (1988).
7. Y. K. Wen, Approximate method for non-linear random vibration. J. Eng. Mech. Div. 4, 389-401 (1975).
8. Q. Liu and H. G. Davies, The non-stationary response probability density functions of non-linearly damped oscillators subjected to white noise excitations. J. Sound Vibr. 139, 425-435 (1990).
9. Y. Suzuki and R. Minai, Stochastic prediction of maximum earthquake response of hysteretic structures. 7th WCEE Seventh World Conf. on Earth. Eng., Istanbul, Turkey, 6, pp. 697-704 (1980).
10. M. Di Paola, G. Ricciardi and M. Vasta, A method for the probabilistic analysis of non-linear systems. Prob. Engng Mech. 10, 1-10 (1995).
11. C. V. L. Charlier, A new form of the frequency function. Medd. Lunds Astronom. Obs. Ser. II, 51 (1928).
12. R. A. Ibrahim, Parametric Random Vibration. Research Studies Press, Taunton (1985).
13. N. C. Hampl and G. I. Schueller, Probability densities of the response of non-linear structures under stochastic dynamic excitation. Prob. Engng Mech. 4, 2-9 (1989).