Stochastic Response Analysis

The last two decades have seen a considerable interest in the response of structures to stochastic loads such as wind, waves and earthquakes, and numerous papers have been written on the subject. Nonetheless, at least for linear structure, the classical methods of stochastic response analysis rest on rather simple and well-defined basis, namely the evaluation of the correlation functions of the response in terms of the correlation functions of the excitation. The covariance functions of the response are then used to find, e.g., characteristics amplitudes or failure probabilities in terms of first-passage of certain barriers.

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

[2]  Steen Krenk,et al.  Stationary and Transient Response Statistics , 1982 .

[3]  Erik Hector Eugene Joseph Vanmarcke,et al.  First passage and other failure criteria in narrow-band random vibration: a discrete state approach. , 1970 .

[4]  E. Vanmarcke.  Properties of Spectral Moments with Applications to Random Vibration , 1972 .

[5]  Steen Krenk,et al.  Stationary and Transient Response Envelopes , 1983 .

[6]  Richard H. Lyon,et al.  On the Vibration Statistics of a Randomly Excited Hard‐Spring Oscillator , 1960 .

[7]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion II , 1945 .

[8]  J.-N. Yang,et al.  First-excursion probability in non-stationary random vibration. , 1973 .

[9]  J. Roberts.  The covariance response of linear systems to locally stationary random excitation , 1971 .

[10]  Erik H. Vanmarcke,et al.  Structural Response to Earthquakes , 1976 .

[11]  R. Arens,et al.  Complex processes for envelopes of normal noise , 1957, IRE Trans. Inf. Theory.

[12]  H. Tajimi,et al.  Statistical Method of Determining the Maximum Response of Building Structure During an Earthquake , 1960 .

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

[14]  Sami F. Masri.  Response of a Multidegree-of-Freedom System to Nonstationary Random Excitation , 1978 .

[15]  J. Roberts,et al.  An approach to the first-passage problem in random vibration , 1968 .

[16]  J. Dugundji,et al.  Envelopes and pre-envelopes of real waveforms , 1958, IRE Trans. Inf. Theory.

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

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

[19]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[20]  M. C. Bernard,et al.  The First Passage Time Problem for Simple Structural Systems , 1972 .

[21]  Masanobu Shinozuka,et al.  Simulation of Nonstationary Random Process , 1967 .

[22]  Alan G. Davenport,et al.  Gust Loading Factors , 1967 .

[23]  Cinna Lomnitz,et al.  Seismic risk and engineering decisions , 1976 .

[24]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion , 1930 .

[25]  S. Krenk.  Nonstationary Narrow-Band Response and First-Passage Probability , 1979 .

[26]  J. W. Shipley,et al.  The first passage problem for stationary random structural vibration , 1972 .

[27]  N. Wax,et al.  Selected Papers on Noise and Stochastic Processes , 1955 .

[28]  M. Longuet-Higgins.  The distribution of intervals between zeros of a stationary random function , 1962, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[29]  H. J. Stumpf,et al.  Transient Response of a Dynamic System Under Random Excitation , 1961 .

[30]  J. R. Maurer,et al.  Mean-square response of simple mechanical systems to nonstationary random excitation. , 1969 .

[31]  Emanuel Parzen,et al.  Stochastic Processes , 1962 .

[32]  John R. Rice,et al.  On the Distribution of Rises and Falls in a Continuous Random Process , 1965 .

[33]  Dario A. Gasparini,et al.  Response of MDOF Systems to Nonstationary Random Excitation , 1979 .