-19
-
APPENDIX B - THEORY OF OPERATION
A vibrating wire attached to the surface of a deforming body will deform in a like manner.
The deformations alter the tension of the wire and hence also its natural frequency of
vibration (resonance). 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 by the equation:
Where;
Lw 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 Lw inches of wire (pounds).
g is the acceleration of gravity (386 in./sec.2).
3. and:
Where;
is the wire material density (0.283 lb./in.3).
a is the cross sectional area of the wire (in.2).
4. Combining equations 1, 2 and 3 gives:
5. Note that the tension (F) can be expressed in terms of strain, e.g.:
Where;
w is the wire strain (in./in.).
is the Young's Modulus of the wire (30 x 106 Psi).
f
L
F
m
w
1
2
m
W
L g
w
W
aL
w
f
L
Fg
a
w
1
2
F
a
w
