2010.03.19 9307PIEVOL04E

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6 Piezoelectric Ceramics Vol.04

3) Relative

When the ele

electric field

under a cons

dielectric con

defined by D

electric field

Calculation o

Eq. 11. Stati

using an all-p

(

Where

(8.854

t

: Dista

S : Electr

C : Static

E

Where

Kr : Electro

vibrat

length

longit

Kt : Electro

ness v

vibrati

fr : Reson

fa : Antires

εε

33

0

=

K

Kt

K

= ⎛⎝

= ⎛⎝

= ⎛⎝

2

2

2

33

15

π

π

π

fr

N

Hz

=

[]

3

l

fr

N

Hz

=

[]

2

l

b)

Lengthwise vibration

The direction of vibration is perpendicular to the

polarization direction; it is a simple vibration in one

plane only. The coefficient of electromechanical

c)

Longitudinal vibration

The directions of polarization and vibration are the

same, vibration is simple vibration. The electro-

Fig. 1-5

>3(a,b,D)

D

a

b

d)

Thickness vibration

Here, thickness is small compared with the area of the

radiation plane; the effect of vibration is the same as

that of longitudinal vibration. Generally, vibration is in

two directions, and discrimination can be made

between the two. The electromechanical coupling

coefficient for this type of vibration is called Kt.

e)

Shear vibration

The direction of vibration is the same as the

polarization direction. Orientation of the drive field

direction is perpendicular to it. A drive electrode is

located perpendicular to the direction of polarization.

The electromechanical coupling coefficient is

Where

(Hz-m)

(Hz-m)

(Hz-m)

D : Diameter of disc or column (m)

: Length of plate, column, or cylinder (m)

a,b: Width of square plate or column (Hz-m)

t

: Thickness of disc, square plate, or cylinder (m)

D

t

t

b

Fig. 1-6

t

3(a,b,D)

t

Fig. 1-7

fr

N

t

Hz

=

[]

4

fr

N

t

Hz

=

[]

5

· · · · · · · · · · (3)

· · · · · · · · · · (4)

· · · · · · · · · · (5)

t

>4a

a>t

Fig. 1-4

· · · · · · · · · · (2)

2) Coefficient of electromechanical coupling

The coefficient of electromechanical coupling repre-

sents the mechanical energy accumulated in a ceramic

or crystal; it is related to the total electrical input. This

coefficient k can be calculated for each individual

vibration mode by using the resonant (fr or fm) and

antiresonant frequencies (fa or fn) and the applicable

formula shown here:

· · · · · · · · · · · · · · · · · · · · · (6)

· · · · · · · · · · · · · · · · · · · · · · · · · (7)

Kr

fa

fr

fr

K

r

rr

r

fa

fr

=

−

⎛

⎝

⎞

⎠

=

−

=⋅

251

2

31

.

tan

π