Date post: | 14-Jun-2015 |
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Piezoelectric Materials
Dr. Mohammad Tawfik
What is Piezoelectric Material?
• Piezoelectric Material is one that possesses the property of converting mechanical energy into electrical energy and vice versa.
Piezoelectric Materials
• Mechanical Stresses Electrical Potential Field : Sensor (Direct Effect)
• Electric Field Mechanical Strain : Actuator (Converse Effect)
Clark, Sounders, Gibbs, 1998
Conventional Setting
Conductive Pole
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
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.
Applications of Piezoelectric Materials in Vibration Control
Collocated Sensor/Actuator
Self-Sensing Actuator
Hybrid Control
Passive Damping / Shunted Piezoelectric Patches
Passively Shunted Networks
Resonant
Capacitive Switched
Resistive
Modeling of Piezoelectric Structures
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
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)
The Electromechanical Coupling
• Electric permittivity (Farade/m) or (Coulomb/mV)
• d31 is called the electromechanical coupling factor (m/Volt)
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
Using those relations:
• Using the relations:
• Introducing the capacitance:
• Or the electrical admittance:
Vt
sAsAdI
Vt
ds
33131
311111
CsVsAdI 131
YVsAdI 131
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
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
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
Different Conditions
• Similar results could be obtained for the electric properties; electric properties are affected by the mechanical boundary conditions.
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
Other types of Piezo!
1-3 Piezocomposites
3333333
3333333
EeD
Eec
S
E
Active Fiber Composites (AFC)
3333
2
311111
SpC
p
Eeff
vv
evcc
3333
313331
SpC
eff
vv
ee
3333
333333
SpC
S
eff
vv
Actuation Action
• PZT and structure are assumed to be in perfect bonding
Axial Motion of Rods
• In this case, we will consider the case when the PZT and the structure are deforming axially only
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
Zero Voltage case
• From that, we may write the force strain relation to be:
ssaassaa
xEtEt
bF
EAEA
F
2
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