Different types of Piezoceramic-structure interaction models using electro mechanical impedance technique: A review
Venu Gopal Madhav ANNAMDAS University of Pittsburgh, PA
Co-Author: Kiran K. ANNAMDAS University of Miami, FL
SPIE 2009 San Diego
March/11/2009
Different types of Piezoceramic-structure interaction models using electro mechanical impedance technique: A review
Outline •
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
Different types of Piezoceramic-structure INTERACTION models using electro mechanical impedance technique: A review
PZT based Electromechanical Impedance (EMI) principle PZT: surface bonded or embedded + Electric field Structure
PZT
2 3 1
Zďƒ 1 / Admittance (Y)
ďƒ&#x;Finally obtain it
PZT: measures resistance of structure to vibrations
PZT based Electromechanical Impedance (EMI) principle in SHM Z (EMI) ďƒ 1 / Admittance (Y) {Y = Conductance + j (Susceptance)}
Healthy Structure
Y H = G H + j BH
Damaged Structure YD = GD + j BD
Comparison mechanism
Experimental Setup Multiplexer
Specimen
Impedance Analyzer
PZT
1 D model [SDOF] Liang et al., (1994) Assumptions • Mechanical interaction between actuator and structure occurs only at the ends of the actuator. •
1D Model
L
Actuator Impedance Z a = F / V at end points (No electric field) Structure Impedance Z s = − F / V (electric field) F is actuator force V is drive point velocity 8
2 D model [M DOF] Zhou et al (1996)
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)) Za= F / eff. Vel. (No elec. Field)
L
Zs= -F/ eff. Vel. (Elec. Field)
2L
Cont‌10
Different types of Piezoceramic-structure interaction models using electro mechanical impedance technique: A review
2
or Y
Only Extensional Actuation 1 or X
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)
d 24Shear actuation
d 33
Longitudinal actuation
(YZ Plane) Extensional actuation
d 32
E3
d15
E2
Z Y
Face Y
E1 L X
Face Z
Y 2H
W
Extensional actuation
Face X Face Z
Bottom
(XZ Plane)
d 31
Top
X
Shear actuation
3D actuation for embedded and surface bonded PZT Annamdas and Soh (2007), J. of Aerospace, ASCE
THREE DIMENSIONAL (3D) ELECTROMECHANICAL IMPEDANCE MODEL: FORMULATION OF DIRECTIONAL SUM IMPEDANCE (DSI)
-( Z S ) = (Linear impedances) + (Cross impedances)
FX σ X (2 LH ) Z S1 = = u 1 u 1 ZS2
FY σ Y (2WH ) = = u 2 u 2
Z S3
FZ FT − FB = = u 3 u ZB − u ZT
Z12 ≈ − Z 23 Z 31
Z S 1Z S 2 Z S1 + Z S 2 − Z S 3
≈
−
ZS 2Z S 3 Z S1 + Z S 2 − Z S 3
≈
−
Z S 3 Z S1 Z S1 + Z S 2 − Z S 3
THREE DIMENSIONAL (3D) ELECTROMECHANICAL IMPEDANCE MODEL: FORMULATION OF DIRECTIONAL SUM IMPEDANCE (DSI)
Structural Impedance
− Z S = Z S1 + Z S 2 − Z S 3 + 2Z12 − 2Z 23 − 2Z13
(1)
− Z S = ( Z S 1λ1 + Z S 2 λ2 − Z S 3λ3 )
(2)
Response Factors Z S1 λ2 λ1 = Z S1 + Z S 2 − Z S 3
ZS2 ZS3 = λ3 = Z S1 + Z S 2 − Z S 3 Z S1 + Z S 2 − Z S 3
Semi Analytical
THREE DIMENSIONAL (3D) ELECTROMECHANICAL IMPEDANCE MODEL: FORMULATION OF DIRECTIONAL SUM IMPEDANCE (DSI)
FX ,Y , Z = FIK
Linear Impedance FX σ X (2 LH ) Z S1 = = u 1 u 1 ZS2
FY σ Y (2WH ) = = u 2 u 2
Z S3
FZ FT − FB = = u 3 u ZB − u ZT N
u I = ∑ u IK K =1
Net Total Force on Face I
Total Force on Face I of PZT
THREE DIMENSIONAL (3D) ELECTROMECHANICAL IMPEDANCE MODEL: FORMULATION OF DIRECTIONAL SUM IMPEDANCE (DSI)
− Z S = ( Z S 1λ1 + Z S 2 λ2 − Z S 3λ3 )
σ
σ
(2)
σ
2σ X λ1 ∑WK 2 H 2σ Y λ2 ∑ LK 2 H 2σ Z λ3 ∑ LKWK 2 3 = + + 1 u v w Semi-analytical directional stresses
σ 1 λ1 0 σ 0 λ = 2 2 σ 3 Semi _ analytical 0 0 Final Admittance
YA = G + j B
(3)
Response Factors
0 σ X σ 0 Y λ3 Numerical σ Z Analytical
THREE DIMENSIONAL (3D) ELECTROMECHANICAL IMPEDANCE MODEL: FORMULATION OF DIRECTIONAL SUM IMPEDANCE (DSI)
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)
(Surface bonded PZT on a aluminium plate of dimension 10 cm x 10 cm x 2 mm)
(PZT embedded inside epoxy adhesive, which is sandwiched between two aluminium plates) Cont‌32
3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION (Annamdas and Soh 2008), J of Aerospace, ASCE
3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION
N PZT of different dimensions
Y
A
N
= G+ Bj = ∑ Y K =1
A K
N
=∑
K =1
jω L K W K 2H K
[ ε 33 + YR {
d 31λ1 {[ A0 sin kLK − d 31 ] + R[C0 sin kWK − d 32 ] + R[ E0 k cos k 2 H K − d 33 ]} + d 32 λ2 { R[ A0 sin kLK − d 31 ] + [C0 sin kWK − d 32 ] + R[ E0 k cos k 2 H K − d 33 ]} +
d 33λ3 { R[ A0 sin kLK − d 31 ] + R[C0 sin kWK − d 32 ] + [ E0 k cos k 2 H K − d 33 ]} }]
3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION
Case 1
Multiple PZT Specimen
3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION
case2
Multiple PZT Specimen
3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION
Case 3
Multiple PZT Specimen
3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION
Results Case 1
Case 2
Case 3
43
3D EMI MODEL OF PZT– ADHESIVE - STRUCTURE Epoxy adhesive mm3
Al
1
Negligible
100 x 100 x 2
2
10 x 10 x 0.5
3
10 x 10 x 1
Finite element mesh of one-quarter 1
mm3
PZT mm3 10 x10 x 0.3
Finite element mesh of one quarter 2
Results
EMI MODEL OF PZT– ADHESIVE - STRUCTURE
Experimental
Experimental
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).
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