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

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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

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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

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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

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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

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Introduction Theory Experimental Results Conclusion

Measurements

Deflectometry

CCDO

M

P

Q

Deflection fieldsCurvature fields

Slope fields

In phase

/2 lag

d

. d

Experimental

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Introduction Theory Experimental Results Conclusion

Image ProcessingGrid

ImagesAt rest Deformed

Phasesxx

y y

-

Slopes

x

-y

Spatial phase shifting

Experimental

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Introduction Theory Experimental Results Conclusion

Experimental set up

Experimental

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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

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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

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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.

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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

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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.

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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

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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 %

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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

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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

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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 ???

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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)