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Research Papers

Prediction of Random Self Friction-Induced Vibrations in Uncertain Dry Friction Systems Using a Multi-Element Generalized Polynomial Chaos Approach

[+] Author and Article Information
Lyes Nechak

 ENSISA-MIPS, 12 rue des frères Lumière, Mulhouse, 68093, Francelyes.nechak@uha.fr

Sébastien Berger

 ENSISA-MIPS, 12 rue des frères Lumière, Mulhouse, 68093, Francesebastien.berger@uha.fr

Evelyne Aubry

 ENSISA-MIPS, 12 rue des frères Lumière, Mulhouse, 68093, Franceevelyne.aubry@uha.fr

J. Vib. Acoust 134(4), 041015 (Jun 01, 2012) (14 pages) doi:10.1115/1.4006413 History: Received September 21, 2010; Revised February 09, 2012; Published June 01, 2012; Online June 01, 2012

The prediction of self friction-induced vibrations is of major importance in the design of dry friction systems. This is known to be a challenging problem since dry friction systems are very complex nonlinear systems. Moreover, it has been shown that the friction coefficients admit dispersions depending in general on the manufacturing process of dry friction systems. As the dynamic behavior of these systems is very sensitive to the friction parameters, it is necessary to predict the friction-induced vibrations by taking into account the dispersion of friction. So, the main problem is to define efficient methods which help to predict friction-induced vibrations by taking into account both nonlinear and random aspect of dry friction systems. The multi-element generalized polynomial chaos formalism is proposed to deal with this question in a more general setting. It is shown that, in the case of friction-induced vibrations obtained from long time integration, the proposed method is efficient by opposite to the generalized polynomial chaos based method and constitutes an interesting alternative to the prohibitive Monte Carlo method.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Mechanical system

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Figure 2

Limit cycles corresponding to two values of the friction coefficient

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Figure 3

Instantaneous mean value of the displacement X1

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Figure 4

Instantaneous variance of the displacement X1

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Figure 5

Realization of the system response for μ=0.3

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Figure 6

Realization of the system response for μ=0.33

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Figure 7

Evolution of the displacement X1 with respect to the uniform variable ξ

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Figure 8

Instantaneous mean value of the displacement X1 estimated by the ME-LePC with the NISP technique

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Figure 9

Instantaneous variance of the displacement X1 estimated by the ME-LePC with the NISP technique

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Figure 10

Realization of the LCO for μ=0.3 by the ME-LePC with the NISP technique

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Figure 11

Realization of the LCO for μ=0.33 by the ME-LePC with the NISP technique

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Figure 12

Instantaneous standard deviation of the displacement X1 with the ME-LePC by the NISP technique

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Figure 13

Instantaneous mean value of the displacement X1 estimated with the ME-LePC with the regression technique

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Figure 14

Instantaneous variance of the displacement X1 estimated with the Me-LePC with the regression technique

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Figure 15

Realization of the LCO for μ=0.3 obtained from the ME-LePC with regression technique

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Figure 16

Realization of the LCO for μ=0.33 obtained from the ME-LePC with regression technique

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