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TABLE III:   Symbols
Symbol Description Units
C Capacitance farad
dij Piezoelectric constant m / V º coul / N
di Inner diameter meter (inch)
dia Diameter meter (inch)
dm Mean diameter (do+di) / 2 meter (inch)
do Outer diameter meter (inch)
E Electric field V / m
Îo Permitivity of space (8.85 x 10-12) farad / meter
F Force Newton
fm Frequency of minimum impedance Hz
fn Frequency of maximum impedance Hz
gij Piezoelectric constant Vm / N º m2 / coul
h Height meter (inch)
kij Electromechanical coupling coefficient
K Relative dielectric constant
l Length meter (inch)
N Frequency constant Hz . m (kHz . inch)
n Number
r Density kg / m3
P Pressure N / m2
Qm Mechanical Q
tan d Dielectric loss factor
S Strain m / m
s Elastic compliance coefficient m2 / N
T Stress N / m2
t Thickness meter (inch)
V Voltage volt
w Width meter (inch)
Y Modulus of elasticity N / m2
Zm Impedance at fm ohms

 

 

Fundamental Piezoelectric Action Modes for Common Ceramic Shapes

Table IV on pages 8-9 shows the basic electromechanical actions resulting from an applied voltage and also the voltage generated when an appropriate force is applied. These are the fundamental modes and consider only the stresses pertaining to that mode, with all other stresses equal to zero.

The equations are useful to approximate the displacements and generated voltages at low frequencies and can extend to the static case.

All shapes shown are polarized along the 3 axis.

Caution is suggested in the direct rigorous application of the equations as they are somewhat simplified. Therefore, the results, including capacitance and resonance frequency, are geometry-dependent.

The symbols used are defined in the table above. The values for the piezoelectric parameters d and g and the relative dielectric constant K for each material are shown in Table VII. The values must be in the MKS system of units.

The frequency constants N are listed in Table VIII.

 

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