interaction_pzt_structure model

Venu Gopal Madhav ANNAMDAS University of Pittsburgh, PA

March/11/2009SPIE 2009 San Diego

Different types of Piezoceramic-structure interaction models using electro mechanical impedance technique: A review

Co-Author: Kiran K. ANNAMDAS University of Miami, FL

• Introduction : Background of EMI Technique

• Electro-Mechanical interaction in SDOF • Electro-Mechanical interaction in MDOF - 2D Model of Linear and Cross Impedances - 2D Model of Linear Impedances - 3D Model of Linear and Cross Impedances - Single and Multiple PZT-host structure interaction model • Conclusions Q&A


Outline

13

2

PZT

Structure

PZT based Electromechanical Impedance (EMI) principle

PZT: surface bonded

PZT: measures resistance of structure to vibrations

+ Electric field or embedded

Z 1 / Admittance (Y) Finally obtain it

Different types of Piezoceramic-structure INTERACTION models using electro mechanical impedance technique: A review

Z (EMI) 1 / Admittance (Y)

Healthy Structure YH = GH + j BH

Damaged Structure YD = GD + j BD

Comparison mechanism

PZT based Electromechanical Impedance (EMI) principle in SHM

{Y = Conductance + j (Susceptance)}

Multiplexer

Impedance Analyzer

Specimen

Experimental Setup

PZT

Liang et al., (1994) Assumptions• Mechanical interaction between actuator and structure

occurs only at the ends of the actuator.

• 1D Model

1 D model [SDOF]1 D model [SDOF]

L

8

Actuator Impedance at end points (No electric field)

Structure Impedance (electric field)

F is actuator force

V is drive point velocity

VFZa /

VFZ s /

Zhou et al (1996)

2 D model [M DOF]2 D model [M DOF]

8

Bhalla and Soh (2004)…..Special (simplified) 2D model of Zhou (1996)Assumptions• Mechanical interaction between a bonded actuator and its

host structure occurs along entire boundary of the patch.

• Plane X-Y

2L

2L

Effective displacement and effective velocity terms

Instead of drive point velocity (Liang et al (1994))

2L

L Za= F / eff. Vel. (No elec. Field)

Zs= -F/ eff. Vel. (Elec. Field)

Cont…10

Only Extensional Actuation

1 or X

2 or Y


2D Stress Model (Bhalla and Soh 2004)

• Very small structure

• Poor peak matching

3D Model L x W x T (mm3)

1 10 x 10 x 0.5

2 10 x 10 x 2

3 15 x15 x 0.5

4 15 x 15 x 2

Raja et al (2004)

Longitudinal actuation

Face X

Extensional actuation

X

Shear actuation

(XZ Plane)

ZFace Y

Face ZTop

Face ZBottom

LY

X

W

2H

Extensional actuation

15d

33d

31d

32d

1EY

3E

Shear actuation

(YZ Plane)24d

2E

3D actuation for embedded and surface bonded PZTAnnamdas and Soh (2007), J. of Aerospace, ASCE

SZ-( ) = (Linear impedances) + (Cross impedances)

222

)2(uWH

uF

Z YYS

ZTZB

BTZS uu

FFuF

Z

33

111

)2(u

LHuFZ XX

S

12Z 321

21

SSS

SS

ZZZZZ

23Z 321

32

SSS

SS

ZZZZZ

31Z 321

13

SSS

SS

ZZZZZ

THREE DIMENSIONAL (3D) ELECTROMECHANICAL IMPEDANCE MODEL:

FORMULATION OF DIRECTIONAL SUM IMPEDANCE (DSI)

321

11

SSS

S

ZZZZ

321

22

SSS

S

ZZZZ

321

33

SSS

S

ZZZZ

)( 332211 SSSS ZZZZ

Response Factors

132312321 222 ZZZZZZZ SSSS (1)

(2)



Structural Impedance

Semi Analytical

IKZYX FF ,,

N

KIKI uu

1

Linear Impedance

Net Total Force

on Face I

Total Force on Face I of PZT

222

)2(uWH

uF

Z YYS

ZTZB

BTZS uu

FFuF

Z

33

111

)2(u

LHuFZ XX

S



Semi-analytical directional stresses

wWL

vHL

uHW KKZKYKX

321 22222

AnalyticalZ

Y

X

NumericalanalyticalSemi

3

2

1

_3

2

1

000000

YA = G + j B

Final Admittance

)( 332211 SSSS ZZZZ (2)

(3)

Response Factors



1 2 3



Analytical + Numerical

Dimensions

10 cm x 10 cm x 2 mm

5 cm x 5 cm x 5 mm

• reasonably large structures

•Surface +Emb.

•Ext. + Long. act

•Good peak pred.

•Rec / sq PZT

•Elec. Iso / anisotrophy

(3D Single PZT- host structure model)

(PZT embedded inside epoxy adhesive, which is sandwiched between two aluminium plates)

(Surface bonded PZT on a aluminium plate of dimension 10 cm x 10 cm x 2 mm)

Cont…32

3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION

(Annamdas and Soh 2008), J of Aerospace, ASCE

AY

N

K

AKY

1

N

K K

KK

HWLj

1 2

33 RY= G+ Bj =

[ + {

]2cos[]sin[]sin[ 330320310131 dHkkERdkWCRdkLAd KKK +

]2cos[]sin[]sin[ 330320310232 dHkkERdkWCdkLARd KKK +

]2cos[]sin[]sin[ 330320310333 dHkkEdkWCRdkLARd KKK }]

N PZT of different dimensions


Multiple PZT Specimen

Case 1



case2



Case 3


Case 1

Case 2

Case 3

Results3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION

Epoxy adhesive mm3

Al mm3

PZT mm3

1 Negligible 100 x 100 x 2 10 x10 x 0.32 10 x 10 x 0.53 10 x 10 x 1

Finite element mesh of one-quarter 1 Finite element mesh of one quarter 2

3D EMI MODEL OF PZT– ADHESIVE - STRUCTURE

43

ResultsExperimental Experimental

EMI MODEL OF PZT– ADHESIVE - STRUCTURE

Conclusions

1. Safety, reliability are important for SHM. Especially for those structures which involve human traffic and huge investments such as the aerospace structures and bridges.

2. In the recent past, PZT has evolved as an efficient smart material which was usually employed in EMI technique. This involves smart interaction of PZT with host structure to be monitored.

3. Many types of SDOF and MDOF based PZT structure interaction models, i.e 1D, 2D and 3D are presented. Any type of model developed by previous researchers or any type of model to be developed by new researchers belongs to one of these interaction models.

4. These models, consider PZT to be negligible in mass in SDOF interaction models where as considers in MDOF interaction models.

5. Epoxy underneath the PZT is either negligible or considerable depending on the type of interaction model. However surface bonded models may ignore mass, stiffness and damping of PZT and epoxy underneath if it is a single PZT. Whereas if PZT needs to be embedded.

6. Additional protections (like casings) have to be wrapped and may increase the over all mass of PZT and thus its mass has to be considered in the formulations.

7. Finally, if the interaction is based on multiple PZT, the admittance signature depends on, the number of PZTs which are active (actuating and sensing). Additionally, it should be noted that the passive (non actuating or sensing) PZTs on host structure can considerably increase the load on the structure to be monitored.

8. Thus, interaction mechanism of PZT-structure depends on many factors like, type of host structure to be monitored (1D, 2D and 3D), number of active and passive PZTs (single or multiple) and type of bonding (surface bonded or embedded).

for your attention

interaction_pzt_structure model

Documents

d model of zhou

d model of linear impedances

structure interaction

review2d stress model

x w x t mm3

gh j bhdamaged structure

pztthree dimensional

cross impedances single