Page 91 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

78 Harmonically Excited Vibration Chap. 3

Figure 3.10-1.
or

+ (3I0-1)

Solving for (o)/(o^y, we have
= (1 - 2^^) ± (3.10-2)

Assuming ^ 1 and neglecting higher-order terms of we arrive at the result

— ) = l ± 2 ^ (3.10-3)
I
Letting the two frequencies corresponding to the roots of Eq. (3.10-3) be iOj and
CO2, we obtain
a>9 —CO 1 _

The quantity Q is then defined as
/'ft fn
Q = (3.10-4)
"2 “ "i f i - f i 2^
Here, again, equivalent damping can be used to define Q for systems with other
forms of damping. Thus, for structural damping, Q is equal to
1
Q = (3.10-5)

3.11 VIBRATION-MEASURING INSTRUMENTS
The basic element of many vibration-measuring instruments is the seismic unit of
Fig. 3.11-1. Depending on the frequency range utilized, displacement, velocity, or
acceleration is indicated by the relative motion of the suspended mass with respect
to the case.