Probability density and excursions of structural response to imperfectly periodic excitation / M. F. Dimentberg in Journal of engineering mechanics, Vol. 133 N°9 (Septembre 2007)  

Public ISBD [article]  inJournal of engineering mechanics > Vol. 133 N°9 (Septembre 2007) . - pp.1037–1041. Titre : Probability density and excursions of structural response to imperfectly periodic excitation Type de document : texte imprimé Auteurs : M. F. Dimentberg, Auteur ; E. Mo, Auteur ; Arvid Naess, Auteur Année de publication : 2007 Article en page(s) : pp.1037–1041. Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Random processes Vibration Probability density functions Structural response Résumé : 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. ISSN : 0733-9399 En ligne : http://ascelibrary.org/action/showAbstract?page=1037&volume=133&issue=9&journalC [...] [article] Probability density and excursions of structural response to imperfectly periodic excitation [texte imprimé] / M. F. Dimentberg, Auteur ; E. Mo, Auteur ; Arvid Naess, Auteur . - 2007 . - pp.1037–1041. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 133 N°9 (Septembre 2007) . - pp.1037–1041. Mots-clés : Random processes Vibration Probability density functions Structural response Résumé : 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. ISSN : 0733-9399 En ligne : http://ascelibrary.org/action/showAbstract?page=1037&volume=133&issue=9&journalC [...]

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