### Abstract

A robust Petrov-Galerkin finite element method is used to determine the first passage survival probability for simple single degree-of-freedom nonlinear oscillators. No assumptions are made about the narrow-bandedness of the response, width of failure bounds, or magnitude of the nonlinearity. The versatility of the method is illustrated for the classical case of the VanderPol oscillator for various failure bound widths and nonlinearities. The accuracy of the solution is then demonstrated by comparison of the finite element results with Monte Carlo simulation.

Original language | English (US) |
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Title of host publication | Transactions of the International Conference on Structural Mechanics in Reactor Technology |

Publisher | North-Holland |

Pages | 105-110 |

Number of pages | 6 |

ISBN (Print) | 0444869670 |

State | Published - Dec 1 1985 |

### Publication series

Name | Transactions of the International Conference on Structural Mechanics in Reactor Technology |
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Volume | M1-M2 |

ISSN (Print) | 0167-563X |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

Spencer, B. F., & Bergman, L. A. (1985). ON THE FIRST PASSAGE PROBLEM IN RANDOM VIBRATION FOR SIMPLE NONLINEAR OSCILLATORS. In

*Transactions of the International Conference on Structural Mechanics in Reactor Technology*(pp. 105-110). (Transactions of the International Conference on Structural Mechanics in Reactor Technology; Vol. M1-M2). North-Holland.