A. Giraudeau, F. Pierron L.M.P.F. (JE 2381) ENSAM Châlons en Champagne
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Transcript of A. Giraudeau, F. Pierron L.M.P.F. (JE 2381) ENSAM Châlons en Champagne
Identification of stiffness and damping properties of composites from full field measurements
Theory and simulations
A. Giraudeau, F. Pierron
L.M.P.F. (JE 2381)
ENSAM Châlons en Champagne
CompTest2003
A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 2
Scheme
1. Introduction
2. Presentation of the method
3. Virtual Fields
4. Application
5. Simulation & Validation
6. Conclusion
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Introduction
Prediction of vibrating behaviour
Material properties- Stiffness
- Damping
Identification : Experimental Modal Analysis
Modal properties
Anisotropic materials
Heterogenous tests
Number of parameters
Anisotropic material
Isotropic material
Vibrating plates
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Presentation of the method
Extension of the Virtual Fields Method
(Grédiac 1989)
3 Points :
• Excitation set up
• Full field measurements
• Application of the Principle of Virtual Works
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In air
Excitation set up
Plate clamped in one point Sine driven movement
Inertial excitation
In vacuum
Out of plane vibrations
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Full field measurements
Optical methods :- no contact
- fields of out of plane slopes
-1.5
+1.5
m
In air In vacuum
Aluminium plate
Examples : Speckle Interferometry measurements
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Principle of Virtual Works
Virtual works : Internal forces
External forces
Inertial forces
Choice of the Virtuals Fields
(Elastic) (Dissipative)
(Clamping) (Acceleration)
u* : virtual displacement
* : virtual strain tensorVirtual Fields
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Actual fields of displacements
xy
O
z
Harmonic driven movement :
Absolute response :
Amplitude PhaseMode k
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F. E. Simulation
Model : Isotropic and viscoelastic material
m-150
+100
- 0
Rectangular plate
2048 shell elements
Freq.1
26.9 Hz
Mode
Freq.3
150 Hz
- 0
-40m-80
In phase /2 lag
Responses
Real Imaginary
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Actual fields of displacements
xy
O
z
Harmonic driven movement :
Absolute response :
Absolute response in complex notation :
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Choice of the Virtuals Fields
Kinematically admissible :
Actual fields :
Virtual fields :
Complex Virtual Fields
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Virtual works of external forces (VWEF)
VWEF
Clamping :F
u*
VWEF
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Virtual works of internal forces (VWIF)
Thin plate : Love Kirchoff theory Isotropic viscoelastic material
+
-
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Virtual works of inertial forces (VWIF)
Acceleration :
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Summary
Virtual Works Principle : VWIF + VWEF = VWAC
at any time
3 equations
Eq1 (no time dep.)
Eq2 (cos(2t))
Eq3 (sin(2t))
for any combination of u and ur*
i*
6 equations : 4 independants equations
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Identification
Interest for 2 equations :
with :Measured
Choosen
Objective function :
Unknown
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Simulation
Isotropic materialF E model :
Rectangular plate
2048 shell elements
Proportional damping :
Virtual fields : Identification
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Excitation at resonances
Simulation – Results (1)
Proportional damping :-5
=10
Noise level (%p-p)
27 Hz 71 Hz 150 Hz 171 Hz
Frequencies
Rel
ativ
e er
rors
(%
)0
5
-5
DxxDxy
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Excitation at resonances
Simulation – Results (2)
Proportional damping :-3
=10
Noise level (%p-p)
27 Hz 71 Hz 150 Hz 171 Hz
Frequencies
Rel
ativ
e er
rors
(%
)0
5
-5
DxxDxyDxy
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Simulation – Results (3)
Proportional damping :-3
=10
Excitation at
NON resonance
Noise level (%p-p)
50 Hz 100 Hz 150 Hz 200 Hz
Frequencies
Rel
ativ
e er
rors
(%
)0
5
-5
DxxDxyDxy
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Conclusion
Simultaneous identification of stiffness and damping
Material damping
Plate of any shape
Resonant or non resonant response
Set of specimens
Excitation on a range of frequencies
Identification of frequency dependance of damping
Anisotropic plates