First passage of uncertain single degree-of-freedom nonlinear oscillators. (English) Zbl 0948.70019
Summary: We examine the first passage of uncertain single degree-of-freedom nonlinear oscillators subjected to random excitation. Statistical fourth moment method is developed to determine first four moments of system response and state function. Distribution function of the system state function is approximately determined by the standard normal distribution functions using Edgeworth series technique, and the reliability is obtained.
MSC:
| 70L05 | Random vibrations in mechanics of particles and systems |
| 70K40 | Forced motions for nonlinear problems in mechanics |
Keywords:
statistical fourth moment method; Edgeworth series technique; random excitation; state function; standard normal distribution functions; reliabilityReferences:
| [1] | Lin, Y. K., Probabilistic Theory of Structural Dynamics (1967), McGraw-Hill: McGraw-Hill New York · Zbl 0359.70052 |
| [2] | Adomian, Stochastic Systems (1983), Academic Press: Academic Press New York |
| [3] | Yang, J.-N.; Shinozuka, M., First passage time problem, J. Acoust. Soc. Am., 47, 393-394 (1970) |
| [4] | Crandall, S. H., First crossing probabilities of the linear oscillator, J. Sound Vib., 12, 285-299 (1970) · Zbl 0195.54504 |
| [5] | Crandall, S. H.; Chandiramani, K. L.; Cook, R. G., Some first-passage problems in random vibration, J. Appl. Mech., 33, 532-538 (1966) |
| [6] | Yang, J. N.; Shinozuka, M., On the first excursion probability in stationary narrow-band random vibration I, J. Appl. Mech., 38, 1017-1022 (1971) · Zbl 0249.70023 |
| [7] | Yang, J. N.; Shinozuka, M., On the first excursion probability in stationary narrow-band random vibration II, J. Appl. Mech., 39, 733-738 (1972) · Zbl 0264.70029 |
| [8] | Roberts, J. B., First passage time for the envelope of a randomly excited linear oscillator, J. Sound Vib., 46, 1-14 (1976) |
| [9] | Bergman, L. A.; Heinrich, J. C., On the reliability of linear oscillator and systems of coupled oscillators, Int. J. Numer. Methods Engrg., 18, 1271-1295 (1982) · Zbl 0499.70036 |
| [10] | Spencer, B. F.; Elishakoff, I., Reliability of uncertain linear and nonlinear systems, J. Engrg. Mech. ASCE, 114, 1, 135-148 (1988) |
| [11] | Ang, A. H.S.; Tang, W. H., Probability Concepts in Engineering Planning and Design, (Basic Principles, Volume I (1975), Wiley: Wiley New York) |
| [12] | Cramer, H., Mathematical Methods of Statistics (1964), Princeton University Press: Princeton University Press New Jersey · Zbl 0119.34601 |
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