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APPENDIX B. THEORY OF OPERATION
A vibrating wire attached to the surface of a deforming body will deform in a manner similar to
that of the body to which it is attached. These deformations alter the tension of the wire,
therefore altering its natural frequency of vibration (resonance).
The examples below are calculated using the Model 4200 gage parameters. Substitute the values
from Table 8 for Models 4202 and 4204. These equations do not apply to Models 4210, 4212,
and 4214.
Model:
Gage Length (L g ):
Wire Length (L w ):
Gage Factor:
The relationship between frequency (period) and deformation (strain) is described as follows:
1) The fundamental frequency (resonant frequency) of vibration of a wire is related to its tension,
length, and mass. The fundamental frequency may be determined by the equation:
Where;
L w is the length of the wire in inches.
F is the wire tension in pounds.
m is the mass of the wire per unit length (pounds, sec. 2 /in. 2 ).
2) Note that:
Where;
W is the weight of L w inches of wire (pounds).
g is the acceleration of gravity (386 in./sec. 2 ).
3) And:
Where;
ρ is the wire material density (0.283 lb./in. 3 ).
a is the cross-sectional area of the wire (in. 2 ).
4200/4200HT
6.000 inches
5.875 inches
3.304
Table 8 - Embedment Strain Gage Theoretical Parameters
f =
m =
W = ρaL
4202
2 inches
2 inches
0.391
�
1
F
2L
m
W
W
L
g
w
w
4204
4.000 inches
3.875 inches
1.422
23
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