### Resumé

Originalsprog | Engelsk |
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Forlag | Institut for Bygningsteknik, Aalborg Universitetscenter |
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Antal sider | 16 |

Status | Udgivet - 1986 |

Navn | Structural Reliability Theory |
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Nummer | R8618 |

Vol/bind | 21 |

ISSN | 0105-7421 |

### Fingerprint

### Emneord

- Random Vibration
- Stochastic Processes
- First Passage Failure
- Bimodal Processes
- Integral Equations

### Citer dette

*Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods*. Institut for Bygningsteknik, Aalborg Universitetscenter. Structural Reliability Theory , Nr. R8618, Bind. 21

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*Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods*. Structural Reliability Theory , nr. R8618, bind 21, Institut for Bygningsteknik, Aalborg Universitetscenter.

**Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods.** / Nielsen, Søren R.K.; Sørensen, John Dalsgaard.

Publikation: Bog/antologi/afhandling/rapport › Rapport › Forskning

TY - RPRT

T1 - Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods

AU - Nielsen, Søren R.K.

AU - Sørensen, John Dalsgaard

PY - 1986

Y1 - 1986

N2 - Close approximations to the first passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first passage probability density function and the distribution function for the time interval spent below a barrier before outcrossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval, and hence for the first passage probability density. The results of the theory agree well with simulation results for narrow banded processes dominated by a single frequency, as well as for bimodal processes with 2 dominating frequencies in the structural response.

AB - Close approximations to the first passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first passage probability density function and the distribution function for the time interval spent below a barrier before outcrossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval, and hence for the first passage probability density. The results of the theory agree well with simulation results for narrow banded processes dominated by a single frequency, as well as for bimodal processes with 2 dominating frequencies in the structural response.

KW - Random Vibration

KW - Stochastic Processes

KW - First Passage Failure

KW - Bimodal Processes

KW - Integral Equations

KW - Random Vibration

KW - Stochastic Processes

KW - First Passage Failure

KW - Bimodal Processes

KW - Integral Equations

M3 - Report

T3 - Structural Reliability Theory

BT - Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods

PB - Institut for Bygningsteknik, Aalborg Universitetscenter

ER -