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

By Alain Bensoussan, Laurent Mertz and Phillip Yam

Abstract

International audienceEarlier 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

Topics: diff usion ergodique, in équations variationnelles stochastiques, équations aux dériv ees partielles avec des conditions non-locales, vibrations aléatoires, diff usion ergodique., [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], [ SPI.MECA.VIBR ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Vibrations [physics.class-ph], [ PHYS.MECA.VIBR ] Physics [physics]/Mechanics [physics]/Vibrations [physics.class-ph]
Publisher: Elsevier
Year: 2012
DOI identifier: 10.1016/j.crma.2012.09.020
OAI identifier: oai:HAL:hal-00653123v1
Provided by: Hal-Diderot

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