Page 121 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

108 Transient Vibration Chap. 4

Figure 4.6-1. Shock puises bounded by a rectangular pulse.
4.6 SHOCK ISOLATION

For shock isolation, the maximum peak response or the transmissibility must be
less than unity. Thus, for the rectangular pulse, this requires [see Eq. (4.5-3)]
7Tt.
2 sm ---- <1.0
T
— < 3 0 - - x 6
T
Vibration isolation is then possible for

h 1
<
T 6
77
377
<
and the natural period of the isolated system must be greater than six times the
pulse time.
Next, consider a more general pulse bounded by a rectangular pulse, such as
those shown in Fig. 4.6-1. The impmlse of these force pulses is clearly less than that
of the rectangular pulse. By remembering that the impulse is equal to the change
in momentum, it is reasonable to assume that the maximum peak response of the
rectangular pulse must be the upper bound to that of the enclosed pulse of general
shape. We also find that for small t^/r, the peak response occurs in the region
t > t y For small values of t ^ / r , the response approaches that of a system excited
by an impulse and the shape of the pulse becomes less important other than to
determine the magnitude of the impulse. Such information is, of course, of
considerable value to the designer in avoiding some difficult mathematical calcula­
tions.

4.7 FINITE DIFFERENCE NUMERICAL COMPUTATION

When the differential equation cannot be integrated in closed form, numerical
methods must be employed. This may well be the case when the system is