### Abstract

The problem considered is that of a second-order differential equation with stochastic parameters. Time-dependent random coefficients may assume both positive and negative values when modeling parametric excitations. As there is no exact solution in the case of colored noise random coefficients, one must use approximate techniques. We presently investigate an iterative procedure. The quality of this approximation to the exact solution is verified with a Monte Carlo simulation. The particular example considered is that of a harmonic oscillator with a time-dependent random stiffness and excited by an external random forcing function. After a brief review of the iterative method, and an outline of the design of the Monte Carlo simulation, an extensive parametric study is presented to establish ranges of parameter values for which the approximation is valid. This comparison study leads to a design criterion for the mathematical modeling of structures with parametric uncertainties. We are interested in using information from studies such as this to understand the behavior of large-scale structures.

Original language | English (US) |
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Pages (from-to) | 173-178 |

Number of pages | 6 |

Journal | Journal of Guidance, Control, and Dynamics |

Volume | 11 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1988 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Aerospace Engineering
- Space and Planetary Science
- Electrical and Electronic Engineering
- Applied Mathematics

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## Cite this

*Journal of Guidance, Control, and Dynamics*,

*11*(2), 173-178. https://doi.org/10.2514/3.20288