THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

20.5 Vibration Control 601Figure 20.8. Plot of transmissibility versus frequency ration f/f n as a function of thedamping ratio of a linear system with one degree of freedom.the natural frequency ω/ω n , and transmissibility T . If the ratio ω/ω n < √ 2, thentransmissibility T > 1, which means that the input disturbance is amplified, notdecreased. In the region ω/ω n > √ 2, T decreases with increasing ξ. At resonancecondition ω/ω n , = 1, transmissibility can be quite large. The region ω/ω n > 2isthe only domain where isolation is possible, and there T (which is less than unity)decreases with decreasing ξ, and this indicates that better isolation can be achievedwith very little or no damping.The curves of Figure 20.8 thus demonstrate the effectiveness of an isolator inmitigating vibration. It is also apparent that isolators should be selected to avoidexciting the natural frequencies of the system, and that damping is important inthe range of resonance, when the system is operating near resonance or merelypassing through resonance during startup. From scrutiny of the isolation region it isnoted that the larger the ratio ω/ω n (or the smaller the value of ω n ), the smaller thetransmissibility will be. From the relation of Equation (20.7), ω n can be made quite