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Preprint, Working Paper, Document sans référence, etc. |
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| Domaine : |
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| Titre : |
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Behavior of the plastic deformation of an elasto-perfectly-plastic oscillator with noise. |
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| Auteur(s) : |
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Alain Bensoussan 1, Laurent Mertz ( ) 2 |
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| Laboratoire : |
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| Résumé : |
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Earlier works in engineering, partly experimental, partly computational have revealed that asymptotically, when the excitation is a white noise, plastic deformation and total deformation for an elasto-perfectly-plastic oscillator have a variance which increases linearly with time with the same coefficient. In this work, we prove this result and we characterize the corresponding drift coefficient. Our study relies on a stochastic variational inequality governing the evolution between the velocity of the oscillator and the non-linear restoring force. We then define long cycles behavior of the Markov process solution of the stochastic variational inequality which is the key concept to obtain the result. An important question in engineering is to compute this coefficient. Also, we provide numerical simulations which show successful agreement with our theoretical prediction and previous empirical studies made by engineers. |
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Langue du texte
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Anglais |
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Date de production,
écriture : |
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01/09/2011 |
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| Mots Clés : |
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in équations variationnelles stochastiques – équations aux dériv ees partielles avec des conditions non-locales – vibrations aléatoires – diff usion ergodique. |
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| Contrat, financement : |
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This research was partially supported by a grant from CEA, Commissariat á l'énergie atomique and by the National Science Foundation under grant DMS-0705247. A large part of this work was completed while one of the authors was visiting the University of Texas at Dallas and the Hong-Kong Polytechnic University. We wish to thank warmly these institutions for the hospitality and support. |
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