Probability Density and Excursions of Structural Response to Imperfectly Periodic Excitation
Publication: Journal of Engineering Mechanics
Volume 133, Issue 9
Abstract
A single-degree-of-freedom system under periodic excitation with random phase modulation is considered. Probability density functions (PDF) of the response are obtained numerically using the path integration method. Basic results are presented in the form of expected number of excursions over a given displacement level. They clearly illustrate the transformation of the response PDF with increasing excitation/system bandwidth ratio from one corresponding to the sinusoid with random phase at small values to asymptotically Gaussian PDF at high values of the above ratio. While this qualitative trend is known from previous analysis of the response excess factor by the method of moments, the present quantitative results may be of direct use for reliability predictions. An analytical study is also made for reduced stochastic differential equations of motion, as obtained by stochastic averaging, by the method of moments resulting in a simple explicit expression for the mean square amplitude.
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Acknowledgments
The first writer contributed to this work during his stay at the Centre for Ships and Ocean Structures (CeSOS) at NTNU. The financial support provided by CeSOS is most highly appreciated.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 9 • September 2007
Pages: 1037 - 1041
Copyright
© 2007 ASCE.
History
Received: Jan 11, 2006
Accepted: Mar 6, 2007
Published online: Sep 1, 2007
Published in print: Sep 2007
Notes
Note. Associate Editor: Roger G. Ghanem
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