Abstract
An analytical moment-based method for calculating structural first failure times under non-Gaussian stochastic behavior is proposed. In the method, a power series that constants can be obtained from response moments (skewness, kurtosis, etc.) is used firstly to map a non-Gaussian structural response into a standard Gaussian process, then mean up-crossing rates, mean clump size and the initial passage probability of a critical barrier level by the original structural response are estimated, and finally, the formula for calculating first failure times is established on the assumption that corrected up-crossing rates are independent. An analysis of a nonlinear single-degree-of-freedom dynamical system excited by a Gaussian model of load not only demonstrates the usage of the proposed method but also shows the accuracy and efficiency of the proposed method by comparisons between the present method and other methods such as Monte Carlo simulation and the traditional Gaussian model.
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Abbreviations
- ν + :
-
mean up-crossing rate
- ν 0 :
-
mean rate of structural response cycles
- ω 0 :
-
undamped natural frequency of a dynamical system
- E(·):
-
mean value of a random variable
- X(t):
-
stochastic process
- U(t):
-
standard Gaussian process
- μ x (t):
-
the mean value function of a stochastic process
- σ x (t):
-
the standard deviation function of a stochastic process
- α 3(t):
-
the skewness coefficient function of a stochastic process
- α 4(t):
-
the kurtosis coefficient function of a stochastic process
- α i (t):
-
the contents in power series
- Φ(·):
-
CDF of standard normal variable
- P f (0):
-
initial passage probability
- S cs :
-
clump size
- 〈S cs〉:
-
mean clump size
- Q(t):
-
stationary, zero mean Gaussian model of load
- ζ:
-
damp ration
- N C :
-
cut-off point
- P f (T):
-
probability of structural first failure times.
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Communicated by DING Hao-jiang
Project supported by the National Natural Science Foundation of China (No. 50478017)
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He, J. Structural first failure times under non-Gaussian stochastic behavior. Appl. Math. Mech.-Engl. Ed. 28, 1487–1494 (2007). https://doi.org/10.1007/s10483-007-1108-9
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DOI: https://doi.org/10.1007/s10483-007-1108-9