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Identification of material properties using full field measurements on vibrating plates
Mr Baoqiao GUO, Dr Alain GIRAUDEAU, Prof. Fabrice PIERRONLMPF research group
École Nationale Supérieure d’Arts et Métiers (ENSAM)Châlons en Champagne - France
2 / 19
Introduction Theory Experimental Results Conclusion
Presentation of the procedure
Thin plates point clamped
Sine driving movement
Inertial excitation
Full field measurements
Data processing using Virtual Fields Method (V.F.M.)
xyxx DD ,
xyxx BB ,
xxxxxx BjDD
xyxyxy BjDD
Introduction
3 / 19
Introduction Theory Experimental Results Conclusion
k,k,D,Df xyxx
Virtual Fields Method
Thin platesSine vibrating response
MeasuredChosen
xyD
xxD
u,M,Fg uuh ,,
Unknown
Principle of Virtual Work
u*, *=(u*)
Virtual fields
V
*
V
*
V
* dmu.adSu.TdV:
Theory
Constitutive law
,, xyxx DD
Thin plates <=> k
4 / 19
Introduction Theory Experimental Results Conclusion
Actual out of plane deflection:
(x,y,t)
= d.cost + Re [ (wr(x,y) +j.wi(x,y)) . exp(jt) ]
Virtual fields:
(x,y,t) = d.cost + Re [ (wr*(x,y) +j.wi*(x,y)) . exp(jt) ]
Two fields to measure
Theory
+ w(x,y,t)
Plate deformation (bending)Driving mouvement
= d.coswt
Two fields to select
5 / 19
Introduction Theory Experimental Results Conclusion
u,u,hu,Fgk,k,D,Df xyxx
V.W.E.F. = 0
UD
DHG
xy
xx
Measured (w(x,y), k(x,y))
Selected
k*(x,y), w*(x,y)
(,w(x,y),w*(x,y))
2
1
22
1)1(
U
U
D
D
HG
HG
xy
xx
Two selected virtuals fields : VF1, VF2
Theory
6 / 19
Introduction Theory Experimental Results Conclusion
Measurements
Deflectometry
CCDO
M
P
Q
Deflection fieldsCurvature fields
Slope fields
In phase
/2 lag
d
. d
Experimental
7 / 19
Introduction Theory Experimental Results Conclusion
Image ProcessingGrid
ImagesAt rest Deformed
Phasesxx
y y
-
Slopes
x
-y
Spatial phase shifting
Experimental
8 / 19
Introduction Theory Experimental Results Conclusion
Experimental set up
Experimental
9 / 19
Introduction Theory Experimental Results Conclusion
Slope fields
Out of resonance 80 Hz Near resonance 100 Hz
Experimental
Plate : PMMA
200 x 160 x 3 mm3
10 / 19
Introduction Theory Experimental Results Conclusion
Noise filtering: polynomial fitting
Deflection field: integrationCurvature fields: differentiation
Experimental
No data (hole)High gradients: uncertain measurements
Remove data before fitting
11 / 19
Introduction Theory Experimental Results ConclusionExperimental
Use of piecewise virtual fields
3x3 5x5
Zero contribution from the clamping area !
Use of optimal special virtual fields
Avril S., Grédiac M., Pierron F.Sensitivity of the virtual fields method to noisy data, Computational Mechanics, vol. 34, n° 6, pp. 439-452, 2004.
Toussaint E., Grédiac M., Pierron F., The virtual fields method with piecewise virtual fields, International Journal of Mechanical Sciences, vol. 48, n° 3, pp. 256-264, 2006.
12 / 19
Introduction Theory Experimental Results Conclusion
Influence of the degree of the polynomial fitting(80 Hz)
Results
0
4
2
8
6
8 10 12 14 16 18
Choice: degree 10
Polynomial degree
13 / 19
Introduction Theory Experimental Results Conclusion
Reference values
Results
Coupons: PMMA beamsh = 4mm, l = 10mm, L= 107-114mmClamped-free conditionsFree vibrations, first bending mode ~80 Hz
3%2.3%C. Var.
1.08 10-4s
4.90 GPaMean
E
f.
14 / 19
Introduction Theory Experimental Results Conclusion
Reference values
Results
Assumption: constant = 0.3 (manufacturer datasheet) (???)
2xx 1
ED
2xy 1
ED
xxxx D.B xyxy D.B
xx
xy
xx
xy
B
B
D
D
15 / 19
Introduction Theory Experimental Results Conclusion
Influence of number of virtual elements (80 Hz)
Results
reference3 x 3 5 x 5
0
1
2
3
4
5
6
Dxx
GPa
CV # 0.4 %
0,0
0,5
1,0
1,5
2,0
Dxy
GPa
CV # 0.6 %
0
1
2
3
4
5
6
7
Bxx
10-4GPa.s
CV # 4 %
0,0
0,5
1,0
1,5
2,0
2,5
3,0
Bxy
10-4GPa.s
CV # 23 %
16 / 19
Introduction Theory Experimental Results Conclusion
Influence of the frequency
Results
0
1
2
3
4
5
6
Dxx
GPa
0,0
0,5
1,0
1,5
2,0
Dxy
GPa
0
1
2
3
4
5
6
7
Bxx
10-4GPa.s
0,0
0,5
1,0
1,5
2,0
2,5
3,0
Bxy
10-4GPa.s
reference80 Hz 100 Hz
17 / 19
Introduction Theory Experimental Results Conclusion
Influence of the frequency
Results
Out of resonance 80 Hz Near resonance 100 Hz
Poor SNR: take pictures at other times
18 / 19
Introduction Theory Experimental Results Conclusion
Influence of the frequency
Results
reference80 Hz 100 Hz
xy
xy
xx
xx
D
B
D
Btan
0,00
0,02
0,04
0,06
0,08
0,10
xx
xx
D
B
0,00
0,02
0,04
0,06
0,08
0,10
xy
xy
D
B
constant ???Material model ???
19 / 19
Introduction Theory Experimental Results Conclusion
Conclusion
Conclusion
• Novel procedure for damping measurements• At or out-of resonance• Based on full-field slope measurements• Main assets
– Direct method (no updating)
– Insensitive to clamping dissipation
– Poisson’s damping
• Future work– Explore wider range of frequencies
– Apply to anisotropic plates (composites)