1. Piezoelectric Materials
Dr. Mohammad Tawfik

2. What is Piezoelectric
Material?
• Piezoelectric Material is one that possesses
the property of converting mechanical energy
into electrical energy and vice versa.

3. Piezoelectric Materials
• Mechanical Stresses  Electrical Potential
Field : Sensor (Direct Effect)
• Electric Field  Mechanical Strain :
Actuator (Converse Effect)
Clark, Sounders, Gibbs, 1998

4. Conventional Setting
Conductive Pole

5. 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

6. 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.

7. Applications of Piezoelectric Materials in
Vibration Control

8. Collocated
Sensor/Actuator

9. Self-Sensing Actuator

10. Hybrid Control

11. Passive Damping / Shunted
Piezoelectric Patches

12. Passively Shunted Networks
Resistive Resonant
Capacitive Switched

13. Modeling of Piezoelectric
Structures

14. 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   s11 1  d31 E
appears in the electric
relations D  d 31 1  33 E

15. 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)

16. The Electromechanical
Coupling
•  Electric permittivity (Farade/m) or
(Coulomb/mV)
• d31 is called the electromechanical coupling
factor (m/Volt)

17. Manipulating the
Equations
• The electric displacement is Q
D
the charge per unit area: A
• The rate of change of the 1 I
charge is the current: D   Idt 
A As
• The electric field is the
electric potential per unit V
length: E
t

18. Using those relations:
d 31
• Using the  1  s11 1  V
relations: t
A 33 s
I  Ad31s 1  V
• Introducing the t
capacitance: I  Ad31s1  CsV
• Or the electrical
admittance: I  Ad31s1  YV

19. For open circuit (I=0)
• We get: Ad 31s
V  1
Y
• Using that into the 2
Asd
strain relation:  1  s11 1  31
1
tY
• Using the expression
for the electric  d 31 
2
1  s11 1 
  s   1
admittance:
 33 11 

20. The electromechanical
coupling factor
• Introducing the factor ‘k’:  1  s11 1  k  1
2
31
• ‘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

21. Different Conditions
• With open circuit conditions, the stiffness of
the piezoelectric material appears to be higher
(less compliance)
1  s11 1  k 1  s 1
2
31
D
• While for short circuit conditions, the stiffness
appears to be lower (more compliance)
  s11  s  E

22. Different Conditions
• Similar results could be obtained for the
electric properties; electric properties are
affected by the mechanical boundary
conditions.

23. Zero-strain conditions
(S=0)
d 31
• Using the 0  s11 1  V
relations: t
As 33  d 31 
2
I  1  V
t  33 s11 
 
• Introducing the
capacitance:
• Or the electrical
admittance:
 
I  Y 1 k31 V
2

24. Other types of Piezo!

25. 1-3 Piezocomposites
E
 3  c 33 3  e33 E 3
S
D3  e33 3   33 E3

26. Active Fiber Composites (AFC)
v p e31
2
c eff 11  c E11 
v 
C
33  v p S 33 
 33e31
e eff
31 
v C  33  v p S 33
 33 S 33
 eff 33  C

v  33  v p S 33 

27. Actuation Action
• PZT and structure are assumed to be in
perfect bonding

28. Axial Motion of Rods
• In this case, we will consider the case when
the PZT and the structure are deforming
axially only

29. Zero Voltage case
• If the structure is subject to axial force only,
we get:
 a  Ea  a
 s  Es s
• And for the equilibrium:
F  Aa a  As s  Aa Ea a  As Es s
F  Aa a  As s   Aa Ea  As Es  x

30. Zero Voltage case
• From that, we may write the force strain
relation to be:
F F b
x  
Aa Ea  As Es 2t a Ea  t s Es

31. Zero Force case
• In this case, the strain of the of the PZT will be
less than that induced by the electric field
only!   E   E   E   E d V
a a s a p a s a 31
t
 s  Es  s
• For equilibrium, F=0:
V
F  Aa a  As s  Aa Ea s  Aa Ea d31  As Es s  0
V t
Aa Ea d 31
s  t
 Aa Ea  As Es 