Approximate first-passage and extremes of narrow-band Gaussian and non-Gaussian random vibrations

An approximate method for estimating the probability distribution of first-passage times and extreme values of stationary narrow-band random vibrations is presented. The advantage of the method is that explicit, closed from expressions are obtained. The method is applied to the response process of a simple linear oscillator driven by both Gaussian and non-Gaussian random excitations and, by comparison with published simulation results, good agreement is obtained. For the Duffing oscillator, the results of Markov diffusion models are compared with the present method, and the agreement is fairly good.

[1]  E. Vanmarcke.  On the Distribution of the First-Passage Time for Normal Stationary Random Processes , 1975 .

[2]  Arvid Naess,et al.  The effect of the Markov chain condition on the prediction of extreme values , 1984 .

[3]  André Preumont,et al.  On the peak factor of stationary Gaussian processes , 1985 .

[4]  A. Naess.  STATISTICAL ANALYSIS OF SECOND-ORDER RESPONSE OF MARINE STRUCTURES , 1985 .

[5]  M. R. Leadbetter,et al.  Extremes and Related Properties of Random Sequences and Processes: Springer Series in Statistics , 1983 .

[6]  A. B. Mason,et al.  An Approach to the First Passage Problem in Random Vibration , 1983 .

[7]  Masanobu Shinozuka,et al.  On the First-Excursion Probability in Stationary Narrow-Band Random Vibration, II , 1971 .

[8]  E. Gumbel,et al.  Statistics of extremes , 1960 .

[9]  S. Rice.  Mathematical analysis of random noise , 1944 .

[10]  Shen-Ho Tzuang,et al.  First-Passage Approximations for Simple Oscillators , 1980 .

[11]  Yu-Kweng Michael Lin.  Probabilistic Theory of Structural Dynamics , 1976 .

[12]  J. Roberts,et al.  First-passage time for randomly excited non-linear oscillators , 1986 .

[13]  Arvid Naess.  The response statistics of non-linear, second-order transformations to Gaussian loads , 1987 .

[14]  R. Langley.  A first passage approximation for normal stationary random processes , 1988 .

[15]  M. Grigoriu.  Crossings of non-gaussian translation processes , 1984 .

[16]  Arvid Naess,et al.  The joint crossing frequency of stochastic processes and its application to wave theory , 1985 .

[17]  Jann N. Yang,et al.  Approximation to First Passage Probability , 1975 .

[18]  A Naess.  ON THE STATISTICAL ANALYSIS OF SLOW-DRIFT FORCES AND MOTIONS OF FLOATING OFFSHORE STRUCTURES , 1986 .

[19]  J. Roberts,et al.  First passage time for the envelope of a randomly excited linear oscillator , 1976 .

[20]  K. L. Chandiramani,et al.  Some First-Passage Problems in Random Vibration , 1966 .

[21]  S. H. Crandall.  First-crossing probabilities of the linear oscillator , 1970 .

[22]  Arvid Naess,et al.  Prediction of extremes of morison-type loading—An example of a general method , 1983 .