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