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

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 3

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

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 4

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

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 5

In air

Excitation set up

Plate clamped in one point Sine driven movement

Inertial excitation

In vacuum

Out of plane vibrations

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 6

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

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 7

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

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 8

Actual fields of displacements

xy

O

z

Harmonic driven movement :

Absolute response :

Amplitude PhaseMode k

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 9

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

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 10

Actual fields of displacements

xy

O

z

Harmonic driven movement :

Absolute response :

Absolute response in complex notation :

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 11

Choice of the Virtuals Fields

Kinematically admissible :

Actual fields :

Virtual fields :

Complex Virtual Fields

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 12

Virtual works of external forces (VWEF)

VWEF

Clamping :F

u*

VWEF

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 13

Virtual works of internal forces (VWIF)

Thin plate : Love Kirchoff theory Isotropic viscoelastic material

+

-

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 14

Virtual works of inertial forces (VWIF)

Acceleration :

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 15

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

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 16

Identification

Interest for 2 equations :

with :Measured

Choosen

Objective function :

Unknown

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 17

Simulation

Isotropic materialF E model :

Rectangular plate

2048 shell elements

Proportional damping :

Virtual fields : Identification

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 18

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

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 19

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

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 20

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

A. Giraudeau, F. Pierron - CompTest 2003 - Châlons 28-30 / 01 / 2003 21

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