Page 81 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

68 Harmonically Excited Vibration Chap. 3

3.6 VIBRATION ISOLATION
Vibratory forces generated by machines and other causes are often unavoidable;
however, their effects on a dynamical system can be minimized by proper isolator
design. An isolation system attempts either to protect a delicate object from
excessive vibration transmitted to it from its supporting structure or to prevent
vibratory forces generated by machines from being transmitted to its surroundings.
The basic problem is the same for these two objectives, that of reducing the
transmitted force.
Figure 3.5-2 for ¡X/Vl shows that the motion transmitted from the support­

ing structure to the mass m is less than 1 when the ratio co/oj^^ is greater than \/2 .
This indicates that the natural frequency w,, of the supported system must be small
compared to that of the disturbing frequency co. This requirement can be met by
using a soft spring.
The other problem of reducing the force transmitted by the machine to the
supporting structure has the same requirement. The force to be isolated is
transmitted through the spring and damper, as shown in Fig. 3.6-1. Its equation is

F ,= y l ( k x f ^ {co^xf = k X ^ \ + ( ^ 1 (3.6-1)

With the disturbing force equal to sin cot, the value of X in the preceding
equation is
F ,/k
X = (3.6-la)
/h 1 - {ù)/ù)„y\ + [2Cw/w„]

The transmissibility 77?, defined as the ratio of the transmitted force to that of the
disturbing force, is then

F-, 1 -I- ( 2 ^ w /w „ )
TR = (3.6-2)
- + [2iw/w„]

Figure 3.6-1. Disturbing force transmitted through springs and damper.