HAL : hal-00653123, version 1

arXiv : 1112.4125

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Behavior of the plastic deformation of an elasto-perfectly-plastic oscillator with noise.

Alain Bensoussan 1, Laurent Mertz 2

(01/09/2011)

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.

1 :	International Center for Decision and Risk Analysis (ICDRiA)
	University of Texas at Dallas
2 :	Laboratoire Jacques-Louis Lions (LJLL)
	CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI

Domaine

:

Mathématiques/Equations aux dérivées partielles Mathématiques/Probabilités Sciences de l'ingénieur/Mécanique/Vibrations Physique/Mécanique/Vibrations

Mots Clés : in équations variationnelles stochastiques – équations aux dériv ees partielles avec des conditions non-locales – vibrations aléatoires – diff usion ergodique.

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Contributeur : Laurent Mertz <>

Soumis le : Dimanche 18 Décembre 2011, 07:24:34

Dernière modification le : Dimanche 18 Décembre 2011, 08:51:30