Comp Test 2003 Identification of stiffness and damping

  • Slides: 21
Download presentation
Comp. Test 2003 Identification of stiffness and damping properties of composites from full field

Comp. Test 2003 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 A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003

Scheme 1. Introduction 2. Presentation of the method 3. Virtual Fields 4. Application 5.

Scheme 1. Introduction 2. Presentation of the method 3. Virtual Fields 4. Application 5. Simulation & Validation 6. Conclusion A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 2

Introduction Prediction of vibrating behaviour Material properties - Stiffness - Damping Identification : Experimental

Introduction Prediction of vibrating behaviour Material properties - Stiffness - Damping Identification : Experimental Modal Analysis Modal properties Anisotropic materials Number of parameters Vibrating plates Heterogenous tests Isotropic material Anisotropic material A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 3

Presentation of the method § Extension of the Virtual Fields Method (Grédiac 1989) §

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 - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 4

Excitation set up Plate clamped in one point Inertial excitation Sine driven movement Out

Excitation set up Plate clamped in one point Inertial excitation Sine driven movement Out of plane vibrations In air In vacuum A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 5

Full field measurements Optical methods : - fields of out of plane slopes -

Full field measurements Optical methods : - fields of out of plane slopes - no contact Examples : Speckle Interferometry measurements Aluminium plate +1. 5 mm In air In vacuum A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 -1. 5 6

Principle of Virtual Works Virtual works : Internal forces (Elastic) (Dissipative) displacement u* :

Principle of Virtual Works Virtual works : Internal forces (Elastic) (Dissipative) displacement u* : virtual e* : virtual strain tensor External forces Inertial forces (Clamping) (Acceleration) Virtual Fields Choice of the Virtuals Fields A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 7

Actual fields of displacements y § Harmonic driven movement : x O § Absolute

Actual fields of displacements y § Harmonic driven movement : x O § Absolute response : z Amplitude Mode k A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 Phase 8

F. E. Simulation Rectangular plate Model : Isotropic and viscoelastic material 2048 shell elements

F. E. Simulation Rectangular plate Model : Isotropic and viscoelastic material 2048 shell elements Responses Mode In phase p/2 lag -0 Freq. 1 -40 26. 9 Hz -80 Real mm Imaginary +100 Freq. 3 - 0 150 Hz -150 A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 9 mm

Actual fields of displacements y x § Harmonic driven movement : O z §

Actual fields of displacements y x § Harmonic driven movement : O z § Absolute response : § Absolute response in complex notation : A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 10

Choice of the Virtuals Fields § Kinematically admissible : Actual fields : Virtual fields

Choice of the Virtuals Fields § Kinematically admissible : Actual fields : Virtual fields : Complex Virtual Fields A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 11

Virtual works of external forces (VWEF) VWEF Clamping : F u* VWEF A. Giraudeau,

Virtual works of external forces (VWEF) VWEF Clamping : F u* VWEF A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 12

Virtual works of internal forces (VWIF) § Thin plate : Love Kirchoff theory §

Virtual works of internal forces (VWIF) § Thin plate : Love Kirchoff theory § Isotropic viscoelastic material + A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 13

Virtual works of inertial forces (VWIF) Acceleration : A. Giraudeau, F. Pierron - Comp.

Virtual works of inertial forces (VWIF) Acceleration : A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 14

Summary Virtual Works Principle : VWIF + VWEF = VWAC § at any time

Summary Virtual Works Principle : VWIF + VWEF = VWAC § at any time 3 equations Eq 1 (no time dep. ) Eq 2 (cos(2 wt)) Eq 3 (sin(2 wt)) § for any combination of u*r and u*i 6 equations : 4 independants equations A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 15

Identification § Interest for 2 equations : with : Measured Choosen Unknown § Objective

Identification § Interest for 2 equations : with : Measured Choosen Unknown § Objective function : A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 16

Simulation F E model : Rectangular plate Isotropic material Proportional damping : b 2048

Simulation F E model : Rectangular plate Isotropic material Proportional damping : b 2048 shell elements Virtual fields : Identification A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 17

Simulation – Results (1) -5 b =10 Proportional damping : Dxx b Dxy Excitation

Simulation – Results (1) -5 b =10 Proportional damping : Dxx b Dxy Excitation at resonances Noise level (%p-p) Relative errors (%) 5 0 -5 27 Hz 71 Hz 150 Hz 171 Hz Frequencies A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 18

Simulation – Results (2) Proportional damping : -3 b =10 Excitation at resonances Dxy

Simulation – Results (2) Proportional damping : -3 b =10 Excitation at resonances Dxy b Dxy Dxx Noise level (%p-p) Relative errors (%) 5 0 -5 27 Hz 71 Hz 150 Hz 171 Hz Frequencies A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 19

Simulation – Results (3) Proportional damping : -3 b =10 Dxx Dxy b Dxy

Simulation – Results (3) Proportional damping : -3 b =10 Dxx Dxy b Dxy Excitation at 5 Noise level (%p-p) Relative errors (%) NON resonance 0 -5 50 Hz 100 Hz 150 Hz 200 Hz Frequencies A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 20

Conclusion § Simultaneous identification of stiffness and damping § Material damping § Plate of

Conclusion § Simultaneous identification of stiffness and damping § Material damping § Plate of any shape Aniso § Resonant or non resonant response tropic plates Ø Set of specimens Ø Excitation on a range of frequencies Identification of frequency dependance of damping A. Giraudeau, F. Pierron - Comp. Test 2003 - Châlons 28 -30 / 01 / 2003 21