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Research Papers

Uncertain Friction-Induced Vibration Study: Coupling of Fuzzy Logic, Fuzzy Sets, and Interval Theories

[+] Author and Article Information
Franck Massa

LAMIH UMR CNRS 8201, University of Valenciennes,
Le Mont Houy, F-59313 Valenciennes, France e-mail: franck.massa@univ-valenciennes.fr

Hai Quan Do

LAMIH UMR CNRS 8201, University of Valenciennes,
Le Mont Houy, F-59313 Valenciennes, France e-mail: HaiQuan.Do@univ-valenciennes.fr

Thierry Tison

LAMIH UMR CNRS 8201, University of Valenciennes,
Le Mont Houy, F-59313 Valenciennes, France e-mail: thierry.tison@univ-valenciennes.fr

Olivier Cazier

LAMIH UMR CNRS 8201, University of Valenciennes,
Le Mont Houy, F-59313 Valenciennes, France e-mail: olivier-cazier@neuf.fr

1Corresponding author.

Manuscript received October 23, 2014; final manuscript received March 9, 2015; published online November 20, 2015. Assoc. Editor: Alba Sofi.

ASME J. Risk Uncertainty Part B 2(1), 011008 (Nov 20, 2015) (12 pages) Paper No: RISK-14-1074; doi: 10.1115/1.4030469 History: Received October 23, 2014; Accepted April 28, 2015

This paper presents a complete method to carry out a fuzzy study of a friction-induced vibration system and to analyze the effects of uncertainty on the output data of a stability problem. The proposed approach decomposes the fuzzy problem into interval problems and calculates interval output solutions by optimization. Next, each calculation of the stability problem output data, which is useful during the optimization process, is reanalyzed by integrating fuzzy logic controllers for the static step and homotopy development and projection techniques for the modal step. Finally, the obtained results are compared with Zadeh’s extension principle reference.

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References

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Figures

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Fig. 1

Description of the beam-on-beam system

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Fig. 2

Frequency and growth rate of the studied system

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Fig. 3

Triangular and trapezoidal membership functions

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Fig. 4

Definition of the interval approach

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Fig. 5

Propagation of uncertainty for fuzzy data

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Fig. 6

Computational procedure for the contact problem

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Fig. 7

Flowchart of the proposed uncertainty propagation strategy

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Fig. 8

Definition of fuzzy input parameters

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Fig. 9

Membership functions of normal and tangential contact loads and dynamical friction coefficient after the first step

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Fig. 10

Membership functions of normal and tangential contact loads and dynamical friction coefficient after the second step

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Fig. 11

Membership functions of x-axis and y-axis positions of node C for the second step

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Fig. 12

Membership functions of unstable frequencies

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Fig. 13

Membership functions of the growth rate coefficient

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Fig. 14

Membership function support of frequency and growth rate

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