Langley, RS and Legault, J and Woodhouse, J and Reynders, E (2013) *On the applicability of the lognormal distribution in random dynamical systems.* Journal of Sound and Vibration, 332. pp. 3289-3302. ISSN 0022-460X

## Abstract

This paper is concerned with the probability density function of the energy of a random dynamical system subjected to harmonic excitation. It is shown that if the natural frequencies and mode shapes of the system conform to the Gaussian Orthogonal Ensemble, then under common types of loading the distribution of the energy of the response is approximately lognormal, providing the modal overlap factor is high (typically greater than two). In contrast, it is shown that the response of a system with Poisson natural frequencies is not approximately lognormal. Numerical simulations are conducted on a plate system to validate the theoretical findings and good agreement is obtained. Simulations are also conducted on a system made from two plates connected with rotational springs to demonstrate that the theoretical findings can be extended to a built-up system. The work provides a theoretical justification of the commonly used empirical practice of assuming that the energy response of a random system is lognormal.

Item Type: | Article |
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Subjects: | UNSPECIFIED |

Divisions: | Div C > Applied Mechanics |

Depositing User: | Cron Job |

Date Deposited: | 15 Dec 2015 13:00 |

Last Modified: | 06 May 2016 04:34 |

DOI: | 10.1016/j.jsv.2012.12.041 |