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Stochastic response and stability of a nonintegrable system / Deepak Kumar in Journal of engineering mechanics, Vol. 134 n°8 (Août 2008) 

Public ISBD [article]  in Journal of engineering mechanics > Vol. 134 n°8 (Août 2008) . - pp. 698-702 Titre : Stochastic response and stability of a nonintegrable system Type de document : texte imprimé Auteurs : Deepak Kumar, Auteur ; T. K. Datta, Auteur Année de publication : 2008 Article en page(s) : pp. 698-702 Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Markov  process  Nonlinear  systems  Stability  Stochastic  processes Résumé : For determining the stochastic response and stability of a strongly nonlinear single-degree-of-freedom system using the stochastic averaging technique, the size of excitations should be small such that the response of the system converges weakly to a Markov process. This condition is not often met with practical problems, and therefore, application of this method for obtaining their responses becomes difficult. Further, for systems with nonlinearities that cannot be integrated in closed form, stability analysis by examining the conditions of the two boundaries of the problem is not possible. A semianalytical method along with a weighted residual technique is presented here to circumvent these difficulties and to determine the response and stability of a strongly nonlinear system subjected to sizable stochastic excitation. The weighted residual technique is employed to correct the errors in averaged drift and diffusion coefficients resulting due to the size of the stochastic excitation. Two example problems are solved as illustrations of the method ISSN : 0733-9399 En ligne : http://cedb.asce.org/cgi/WWWdisplay.cgi?166084 [article] Stochastic response and stability of a nonintegrable system [texte imprimé] / Deepak Kumar, Auteur ; T. K. Datta, Auteur . - 2008 . - pp. 698-702. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 134 n°8 (Août 2008) . - pp. 698-702 Mots-clés : Markov  process  Nonlinear  systems  Stability  Stochastic  processes Résumé : For determining the stochastic response and stability of a strongly nonlinear single-degree-of-freedom system using the stochastic averaging technique, the size of excitations should be small such that the response of the system converges weakly to a Markov process. This condition is not often met with practical problems, and therefore, application of this method for obtaining their responses becomes difficult. Further, for systems with nonlinearities that cannot be integrated in closed form, stability analysis by examining the conditions of the two boundaries of the problem is not possible. A semianalytical method along with a weighted residual technique is presented here to circumvent these difficulties and to determine the response and stability of a strongly nonlinear system subjected to sizable stochastic excitation. The weighted residual technique is employed to correct the errors in averaged drift and diffusion coefficients resulting due to the size of the stochastic excitation. Two example problems are solved as illustrations of the method ISSN : 0733-9399 En ligne : http://cedb.asce.org/cgi/WWWdisplay.cgi?166084