### Abstract

This paper reports some of the recent efforts by the authors to examine the random vibration of mechanical systems of large dimension. A finite element solution method for the stationary three-dimensional Fokker-Planck equation, employing sparse storage and iterative solution strategies, is outlined and then applied to several representative systems. The first of these is a linear oscillator subjected to a first order linearly filtered Gaussian white noise process. This problem is used to verify and assess the accuracy of the method. After verification, two Duffing systems are analyzed, one exhibiting unimodal and the other bimodal response characteristics. Finally, some comparisons of the finite element results with those from Monte Carlo simulation are made for the two nonlinear systems.

Original language | English (US) |
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Title of host publication | 15th Biennial Conference on Mechanical Vibration and Noise |

Pages | 939-947 |

Number of pages | 9 |

Volume | 84 |

Edition | 3 Pt A/2 |

State | Published - 1995 |

Event | Proceedings of the 1995 ASME Design Engineering Technical Conference - Boston, MA, USA Duration: Sep 17 1995 → Sep 20 1995 |

### Other

Other | Proceedings of the 1995 ASME Design Engineering Technical Conference |
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City | Boston, MA, USA |

Period | 9/17/95 → 9/20/95 |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*15th Biennial Conference on Mechanical Vibration and Noise*(3 Pt A/2 ed., Vol. 84, pp. 939-947)