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.

References

References
1.
Tison
,
T.
,
Heussaff
,
A.
,
Massa
,
F.
,
Turpin
,
I.
, and
Nunes
,
R. F.
,
2014
, “
Improvement in the Predictivity of Squeal Simulations: Uncertainty and Robustness
,”
J. Sound Vib.
,
333
(
15
), pp.
3394
3412
.10.1016/j.jsv.2014.03.011
2.
Butlin
,
T.
, and , and
Woodhouse
,
J.
,
2010
, “
Friction-Induced Vibration: Quantifying Sensitivity and Uncertainty
,”
J. Sound Vib.
,
329
, pp.
509
526
.10.1016/j.jsv.2009.09.026
3.
Nobari
,
A.
, ,
Ouyang
,
H.
, and , and
Bannister
,
P.
,
2015
, “
Statistics of Complex Eigenvalues in Friction-Induced Vibration
,”
J. Sound Vib.
,
338
, pp.
169
183
.10.1016/j.jsv.2014.10.017
4.
Sarrouy
,
E.
,
Dessombz
,
O.
, and
Sinou
,
J.-J.
,
2013
, “
Stochastic Study of a Non-Linear Self-Excited System With Friction
,”
Eur. J. Mech. A/Solids
,
40
, pp.
1
10
.10.1016/j.euromechsol.2012.12.003
5.
Nechak
,
L.
,
Berger
,
S.
, and
Aubry
,
E.
,
2011
, “
A Polynomial Chaos Approach to Robust Analysis of the Dynamic Behavior of Friction Systems
,”
Eur. J. Mech. A/Solid
,
30
(
4
), pp.
594
607
.10.1016/j.euromechsol.2011.03.002
6.
Meziane
,
A.
,
Baillet
,
L.
, and
Laulagnet
,
B.
,
2010
, “
Experimental and Numerical Investigation of Friction-Induced Vibration of a Beam-on-Beam in Contact With Friction
,”
Appl. Acoust.
,
71
(
9
), pp.
848
853
.10.1016/j.apacoust.2010.04.012
7.
Heussaff
,
A.
,
Dubar
,
L.
,
Tison
,
T.
,
Watremez
,
M.
, and
Nunes
,
R. F.
,
2012
, “
A Methodology for the Modelling of the Variability of Brake Lining Surfaces
,”
Wear
,
289
, pp.
145
159
. 0043-164810.1016/j.wear.2012.04.002
8.
Zadeh
,
L. A.
,
1965
, “
Fuzzy Sets
,”
Infor. Control
,
8
, pp.
338
353
. 0315-598610.1016/S0019-9958(65)90241-X
9.
Moens
,
D.
, and
Hanss
,
M.
,
2011
, “
Non-Probabilistic Finite Element Analysis for Parametric Uncertainty Treatment in Applied Mechanics: Recent Advances
,”
Finite Elem. Anal. Des.
,
47
(
1
), pp.
4
16
.10.1016/j.finel.2010.07.010
10.
Massa
,
F.
,
Ruffin
,
K.
,
Lallemand
,
B.
, and
Tison
,
T.
,
2008
, “
Structural Analysis by Interval Approach
,”
Eur. J. Comput. Mech.
,
17
(
5–7
), pp.
869
880
. 1779-7179
11.
Massa
,
F.
,
Lallemand
,
B.
,
Tison
,
T.
, and
Level
,
P.
,
2004
, “
Fuzzy Eigensolutions of Mechanical Structures
,”
Eng. Comput.
,
21
(
1
), pp.
66
77
.10.1108/02644400410511846
12.
Massa
,
F.
,
Leroux
,
A.
,
Lallemand
,
B.
,
Tison
,
T.
,
Mary
,
S.
, and
Buffe
,
F.
,
2011
, “Fuzzy Vibration Analysis and Optimization of Engineering Structures Application to Demeter Satellite,” (IUTAM Book Series, Vol.
27
, Series 1),
Springer
,
The Netherlands
, pp.
57
69
.
13.
Gonzalez
,
A.
,
Lauber
,
J.
,
Guerra
,
T. M.
,
Massa
,
F.
, and
Tison
,
T.
,
2013
, “
Towards Large Time Simulation Reduction for the Solving of Mechanical Contact (Large Scale) Problems: A Robust Control Approach
,”
Intell. Control Autom. Sci.
,
3
(
1
), pp
417
422
.
14.
Gonzalez
,
A.
,
Lauber
,
J.
,
Guerra
,
T. M.
,
Massa
,
F.
, and
Tison
,
T.
,
2014
, “
Large Time Simulation Reduction for Solving the Mechanical Contact Problem: A Fuzzy Control Approach
,”
World Congr.
,
19
(
1
), pp.
2558
2563
.
15.
Mamdami
,
E. H.
, and
Assilian
,
S.
,
1975
, “
An Experiment in Linguistic Synthesis With a Fuzzy Logic Controller
,”
Int. J. Man Mach. Stud.
,
7
(
1
), pp.
1
13
.10.1016/S0020-7373(75)80002-2
16.
Bingül
,
Z.
, and
Karahan
,
O.
,
2011
, “
A Fuzzy Logic Controller Tuned With PSO for 2 DOF Robot Trajectory Control
,”
Expert Syst. Appl.
,
38
(
1
), pp.
1017
1031
.10.1016/j.eswa.2010.07.131
17.
Massa
,
F.
,
Tison
,
T.
,
Lallemand
,
B.
, and
Cazier
,
O.
,
2011
, “
Structural Modal Reanalysis Methods Using Homotopy Perturbation and Projection Techniques
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
45–46
), pp.
2971
2982
.10.1016/j.cma.2011.06.016
18.
Wang
,
B. P.
,
1991
, “
Improved Approximate Methods for Computing Eigenvector Derivatives in Structural Dynamics
,”
AIAA J.
,
29
(
6
), pp.
1018
1020
. 0001-145210.2514/3.59945
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