Local similarity in nonlinear random vibration

Journal of Applied Mechanics, Transactions ASME

Volumn 66, Issue 1, 1999, Pages 225-235

  Krenk, S ^a   Roberts, J B ^b  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b UNIVERSITY OF SUSSEX   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; DAMPING; DIFFERENTIAL EQUATIONS; OSCILLATORS (MECHANICAL); PROBABILITY; RANDOM PROCESSES; SPURIOUS SIGNAL NOISE; STIFFNESS;

FOKKER-PLANK-KOLMOGOROV EQUATIONS; NON-WHITE WIDE-BAND RANDOM NOISES; NONLINEAR RANDOM VIBRATIONS;

MACHINE VIBRATIONS;

EID: 0033098922     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.2789151     Document Type: Article

References (19)

1. Bouc, R., 1994, “The power spectral density of response for a strongly nonlinear random oscillator,” Journal of Sound and Vibration, Vol. 175, pp. 317-331.
2. Cai, G.Q., 1995, “Random vibration of nonlinear systems under nonwhite excitations,” Journal of Engineering Mechanics, Vol. 121, pp. 633-639.
3. Caughey, T.K., 1971, “Nonlinear theory of random vibrations,” Advances in Applied Mechanics, Vol. 11, C.S. Yih, ed., Academic Press, New York, pp. 209-253.
4. Dimentberg, M., Cai, G.Q., and Lin, Y.K., 1995, “Application of quasi-conservative averaging to a non-linear system under non-white excitation,” International Journal of Non-Linear Mechanics, Vol. 30, pp. 677-685.
5. Fogli, M., Bresollette, P., and Bernard, P., 1996, “The dynamics of a stochastic oscillator with impacts,” European Journal of Mechanics, A Solids, Vol. 15, pp. 213-241.
6. Gardiner, C.W., 1985, Handbook of Stochastic Methods, Springer-Verlag, Berlin.
7. Gradshteyn, I.S., and Ryzhik, I.M., 1965, Table of Integrals Series and Products, Academic Press, New York.
8. Hennig, K., and Roberts, J.B., 1986, “Averaging methods for randomly excited non-linear oscillations,” Random Vibrations—Status and Recent Developments, 1. Elishakoff and R.H. Lyon, eds., Elsevier, Amsterdam, pp. 149-161.
9. Iwan, W.D., and Spanos, P.-T., 1978, “Response Envelope Statistics for Nonlinear Oscillators With Random Excitation,” ASME Journal of Applied Mechanics, Vol. 45.
10. Krenk, S., 1985, “Generalized Hermite polynomials and the spectrum of nonlinear random vibration,” IUTAM Symposium on Probabilistic Methods in the Mechanics of Solids and Structures, S. Eggwertz and N. Lind, eds., SpringerVerlag, Berlin, pp. 71-80.
11. Krenk, S., 1998, “Energy and spectral density in non-linear random response,” Proceedings of the Fourth International Conference on Stochastic Structural Dynamics, Aug. 6-9, Notre Dame, IN, Balkema, Rotterdam.
12. Lin, Y.K., and Cai, G.Q., 1995, Probabilistic Structural Dynamics, McGraw-Hill, New York.
13. Roberts, J.B., 1978, “The energy envelope of a randomly excited non-linear oscillator,” Journal of Sound and Vibration, Vol. 60, pp. 177-185.
14. Roberts, J.B., 1982, “A stochastic theory for nonlinear ship rolling in irregular seas,” Journal of Ship Research, Vol. 26, pp. 229-245.
15. Roberts, J.B., 1983, “Energy methods for non-linear systems with non-white excitation,” IUTAM Symposium on Random Vibrations and Reliability, K. Hennig, ed., Akademie-Verlag, Berlin, pp. 285-294.
16. Roberts, J.B., 1989, “Prediction of ship roll motion in irregular seas using stochastic process theory,” Proceedings of the 47th Session of the International Statistical Institute, Vol. C1, Paris, pp. 497-515.
17. Roberts, J.B., and Spanos, P.D., 1986, “Stochastic averaging: an approximate method of solving random vibration problems,” International Journal of NonLinear Mechanics, Vol. 21, pp. 111-134.
18. Roberts, J.B., and Spanos, P.D., 1990, Random Vibration and Statistical Linearization, John Wiley and Sons, New York.
19. Stratonovich, R.L., 1963, Topics in the Theory of Random Noise, Vols. 1 and 2, Gordon and Breach, New York.