Page 95 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

82 Harmonically Excited Vibration Chap. 3

Figure 3.11-5. Acceleration error vs. frequency with as a parameter.
shows that the factor

1 - + 2^:

approaches unity for co/io„ -> 0, so that
(o^Y acceleration
Z - (3.11-6)

Thus, Z becomes proportional to the acceleration of the motion to be measured
with a factor 1/w^. The useful range of the accelerometer can be seen from Fig.
3.11-5, which is a magnified plot of
1

(ill
1
for various values of damping ¿i. The diagram shows that the useful frequency
range of the undamped accelerometer is somewhat limited. However, with = 0.7,
the useful frequency range is 0 < o)/(o^ < 0.20 with a maximum error less than
0.01 percent. Thus, an instrument with a natural frequency of 100 Hz has a useful
frequency range from 0 to 20 Hz with negligible error. Electromagnetic-type
accelerometers generally utilize damping around = 0.7, which not only extends
the useful frequency range, but also prevents phase distortion for complex waves,
as will be shown later. On the other hand, very high natural-frequency instruments,
such as the piezoelectric crystal accelerometers, have almost zero damping and
operate without distortion up to frequencies of 0.06/„.