Post on 30-Dec-2015
description
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
Identification of local material damping in
vibrating plates using full-field measurements
Alain Giraudeau, Fabrice PIERRON
LMPF research groupArts et Métiers ParisTech
Châlons en Champagne - France
7th International Conference on Modern Practice in Stress and Vibration Analysis, 8-10th September 2009, Cambridge
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
Motivation / Objectives
Material damping Difficult to measure Problem with connections/joints Most of the standard techniques rely on beams Difficult (but important) to get both complex stiffnesses
on same testN.W. Tschoegl, W.G. Knauss, and I. Emri. Poisson's ratio in linear viscoelasticity - a critical review. Mechanics of Time-Dependent Materials, 6:3-51, 2002.
Objectives Simultaneous identification of both complex
stiffnesses (isotropy) on single test Method to cancel the effect of connections Explore the use of full-field measurements
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Identification of material properties :Stiffness
Damping
Thin plate specimens
Dynamic loading
Attachements : Parasistic effects Unknown energy loss
Equilibrium of forces No energy consideration
F(t)
Principle
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
Dynamic equilibrium :
Point M :
iij,ij f
dVudVufdVu ii
V
i
V
ijij
V
,
dVudVufdSuTdV ii
V
i
V
ii
V
ijij
V
*:
Observed area
Internal f. Boundary f. Volumic f. Inertial f.
Principle of Virtual Work (P V W)
:,* yxui- Continuous
- Differentiable
ui* ui*ui*
Principle F(t)
M
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
Considered case
Rectangular thin plate
Sine driving movement
Inertial excitation
Full field measurements
Data processing using Virtual Fields Method (V.F.M.)
Clamped on small area
Principle
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
Principle of Virtual Work
u*
Thin plates Sine vibrating response
*=(u*)
xyD
xxDConstitutive law
,, xyxx DD
uFg , uuh ,,
Unknown
Thin plates <=> k
dVudSuTdV ii
V
ii
V
ijij
V
*:
kkDDf xyxx ,,,
SelectedMeasured
Virtual Fields Method
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
dVudSuTdV ii
V
ii
V
ijij
V
*:
uuhuFgkkDDf xyxx ,,,,,,
along V. F. Selection :
= 0
= 0
uuhkkDDf xyxx ,,,,,
0*
0*u
Virtual Fields Method
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
P V W uuhkkDDf xyxx ,,,,,
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
Direct resolution of an inverse problem
Virtual Fields Method
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
Deflectometry
CCDO
M
P
Q
Deflection fieldsCurvature fields
Slope fields
In phase
/2 lag
d
. d
Experimental arrangement
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
Image Processing
Grid ImagesAt rest Deformed
Phasesxx
y y
-
Slopes
x
-y
Spatial phase evaluation
Experimental arrangement
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
Experimental set-up
Experimental arrangement
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
Rea
lIm
agin
ary
Slope / X
0.41 mrad / col.
Slope / Y
0.17 mrad / col.
Deflection
34 m / col.
80Hz (out of resonance)Images (examples)
Results
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
Piecewise virtual fields (Toussaint et al.,
IJMS, 2006)
w*(x,y) = 0
*(x,y) = 0
Virtual fields selection
Results
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Reference valuesCoupons: polycarbonate beams
h = 4mm, l = 10mm, L= 107-114mm
Clamped-free conditions
Free vibrations, first bending mode
E
(GPa)
( = tan() )
Means 4.900.055
C. variation
2.4% 5.2%
DMTA
0.056
Results
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Results
80 Hz 100 Hz reference (Beams, DMTA)(non res.) (res.)
)ˆ1(h
D12E
3xx
xx
xy
D
Dˆ
0,00
0,02
0,04
0,06
0,08
0,10
tan(delta)
)ERe(
)EIm()tan(
0,00
0,02
0,04
0,06
0,08
0,10
Poisson rat. loss factor
)ˆRe(
)ˆIm(
0
1
2
3
4
5
6
Young mod.
GPa
)ERe(E
0,0
0,1
0,2
0,3
0,4
0,5
Poisson rat.
)ˆRe(
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
Boundary condition effects
Rubber washers
2nd accelerometer
= 34°
tan()=0.672nd accel.
Driving mvt. 100 Hz
Results
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0
1
2
3
4
5
6
Young mod.0,0
0,1
0,2
0,3
0,4
0,5
Poisson rat.
GPa
0,00
0,02
0,04
0,06
0,08
0,10
tan(delta)
0,000
0,020
0,040
0,060
0,080
0,100
Poisson rat. loss factor
Initial clamping With rubber washers
Boundary condition effects (2) 100 Hz
tan()=0.67
Results
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Additional damping effect
Viscoelastic patch at back surface
w*(x,y) = 0
*(x,y) = 0
Results
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
0
1
2
3
4
5
6
Young mod.0,0
0,1
0,2
0,3
0,4
0,5
Poisson rat.
GPa
0,00
0,02
0,04
0,06
0,08
0,10
tan(delta)
0,00
0,02
0,04
0,06
0,08
0,10
Poisson rat. loss factor
Initial clamping With rubber washers
Additional damping effect (2) 100 Hz
Results
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A. Giraudeau, F. Pierron - 2009 MPSVA conference
Conclusion
Simultaneous identification of stiffness and damping
Material damping
Resonant or non resonant response Information on localization phenomena
Low sensitivity to boundary conditions
Could be applied to in-plane vibrations
Plate of any shape Part of a component
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Conclusion
Soundboard of a guitar
Local damping
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Conclusion
Improvements Time synchronization: high speed camera Better fixture (sweep over large frequency range)
Future work Apply to composite plates (anisotropy) Test on more complex structures
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