01 Piezoelectric Material
-
Upload
mohammad-tawfik -
Category
Education
-
view
647 -
download
2
Transcript of 01 Piezoelectric Material
![Page 1: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/1.jpg)
Piezoelectric Materials
Dr. Mohammad Tawfik
![Page 2: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/2.jpg)
What is Piezoelectric Material?
• Piezoelectric Material is one that possesses the property of converting mechanical energy into electrical energy and vice versa.
![Page 3: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/3.jpg)
Piezoelectric Materials
• Mechanical Stresses Electrical Potential Field : Sensor (Direct Effect)
• Electric Field Mechanical Strain : Actuator (Converse Effect)
Clark, Sounders, Gibbs, 1998
![Page 4: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/4.jpg)
Conventional Setting
Conductive Pole
![Page 5: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/5.jpg)
Piezoelectric Sensor
• When mechanical stresses are applied on the surface, electric charges are generated (sensor, direct effect).
• If those charges are collected on a conductor that is connected to a circuit, current is generated
![Page 6: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/6.jpg)
Piezoelectric Actuator
• When electric potential (voltage) is applied to the surface of the piezoelectric material, mechanical strain is generated (actuator).
• If the piezoelectric material is bonded to a surface of a structure, it forces the structure to move with it.
![Page 7: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/7.jpg)
Applications of Piezoelectric Materials in Vibration Control
![Page 8: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/8.jpg)
Collocated Sensor/Actuator
![Page 9: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/9.jpg)
Self-Sensing Actuator
![Page 10: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/10.jpg)
Hybrid Control
![Page 11: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/11.jpg)
Passive Damping / Shunted Piezoelectric Patches
![Page 12: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/12.jpg)
Passively Shunted Networks
Resonant
Capacitive Switched
Resistive
![Page 13: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/13.jpg)
Modeling of Piezoelectric Structures
![Page 14: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/14.jpg)
Constitutive Relations
• The piezoelectric effect appears in the stress strain relations of the piezoelectric material in the form of an extra electric term
• Similarly, the mechanical effect appears in the electric relations EdD
Eds
33131
31111
![Page 15: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/15.jpg)
Constitutive Relations
• ‘S’ (capital s) is the strain
• ‘T’ is the stress (N/m2)
• ‘E’ is the electric field (Volt/m)
• ‘s’ (small s) is the compliance; 1/stiffness (m2/N)
• ‘D’ is the electric displacement, charge per unit area (Coulomb/m2)
![Page 16: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/16.jpg)
The Electromechanical Coupling
• Electric permittivity (Farade/m) or (Coulomb/mV)
• d31 is called the electromechanical coupling factor (m/Volt)
![Page 17: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/17.jpg)
Manipulating the Equations
A
QD
As
IIdt
AD
1
• The electric displacement is
the charge per unit area:
• The rate of change of the
charge is the current:
• The electric field is the
electric potential per unit
length:t
VE
![Page 18: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/18.jpg)
Using those relations:
• Using the relations:
• Introducing the capacitance:
• Or the electrical admittance:
Vt
sAsAdI
Vt
ds
33131
311111
CsVsAdI 131
YVsAdI 131
![Page 19: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/19.jpg)
For open circuit (I=0)
• We get:
• Using that into the strain relation:
• Using the expression for the electric admittance:
131
Y
sAdV
1
2
311111
tY
Asds
1
1133
2
31111 1
s
ds
![Page 20: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/20.jpg)
The electromechanical coupling factor
• Introducing the factor ‘k’:
• ‘k’ is called the electromechanical coupling factor (coefficient)
• ‘k’ presents the ratio between the mechanical energy and the electrical energy stored in the piezoelectric material.
• For the k13, the best conditions will give a value of 0.4
1
2
31111 1 ks
![Page 21: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/21.jpg)
Different Conditions
• With open circuit conditions, the stiffness of the piezoelectric material appears to be higher (less compliance)
• While for short circuit conditions, the stiffness appears to be lower (more compliance)
11
2
31111 1 Dsks
Ess 11
![Page 22: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/22.jpg)
Different Conditions
• Similar results could be obtained for the electric properties; electric properties are affected by the mechanical boundary conditions.
![Page 23: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/23.jpg)
Zero-strain conditions (S=0)
• Using the relations:
• Introducing the capacitance:
• Or the electrical admittance:
Vt
ds 31
1110
Vs
d
t
AsI
1133
2
3133 1
VkYI 2
311
![Page 24: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/24.jpg)
Other types of Piezo!
![Page 25: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/25.jpg)
1-3 Piezocomposites
3333333
3333333
EeD
Eec
S
E
![Page 26: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/26.jpg)
Active Fiber Composites (AFC)
3333
2
311111
SpC
p
Eeff
vv
evcc
3333
313331
SpC
eff
vv
ee
3333
333333
SpC
S
eff
vv
![Page 27: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/27.jpg)
Actuation Action
• PZT and structure are assumed to be in perfect bonding
![Page 28: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/28.jpg)
Axial Motion of Rods
• In this case, we will consider the case when the PZT and the structure are deforming axially only
![Page 29: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/29.jpg)
Zero Voltage case
• If the structure is subject to axial force only, we get:
• And for the equilibrium:
sss
aaa
E
E
sssaaassaa EAEAAAF
xssaassaa EAEAAAF
![Page 30: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/30.jpg)
Zero Voltage case
• From that, we may write the force strain relation to be:
ssaassaa
xEtEt
bF
EAEA
F
2
![Page 31: 01 Piezoelectric Material](https://reader034.fdocuments.us/reader034/viewer/2022052301/557daa19d8b42acb768b4b36/html5/thumbnails/31.jpg)
Zero Force case
• In this case, the strain of the of the PZT will be less than that induced by the electric field only!
• For equilibrium, F=0:sss
asapasaa
E
t
VdEEEE
31
031 sssaasaassaa EAt
VdEAEAAAF
ssaa
aa
sEAEA
t
VdEA
31