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which is sometimes expressed as an isolation efficiency or percent reduction in vibration in Fig. 11.8. This simplification is occasionally encountered in vibration isolation specifications that call for a given percentage of isolation at the operating point. It is better to specify the degree of isolation indirectly by calling out the deflection of the isolator, which is directly measurable by the installing contractor, rather than an efficiency that is abstract and difficult to measure in the field.

It is important to recall that these simple relationships only hold for single degree of freedom systems. If we are talking about a piece of mechanical equipment located on a slab the deflection of the slab under the weight of the isolated equipment must be very low— typically 8 to 10 times less than the deflection of the isolator for this approximation to hold. As the stiffness of the slab decreases, softer vibration isolators must be used to compensate.

When the excitation force is applied directly to the supported object or when it is self excited through eccentric motion, vibration isolators do not decrease the amplitude of the driven object but only the forces transmitted to the support system. When the supported object is excited by the motion of the support base, there is a similar reduction in the forces transmitted to the object. For a given directly applied excitation force, an inertial base consisting of a large mass, such as a concrete slab placed between the vibrating equipment and the support system, can decrease the amplitude of the supported equipment, but interestingly

Figure 11.8 Isolation Efficiency for a Flexible Mount

Figure 11.8 Isolation Efficiency for a Flexible Mount

STATIC* DEFLECTION, inches

not the amplitude of the transmitted force. Inertial bases are very helpful in attenuating the motion of mechanical equipment such as pumps, large compressors, and fans, which can have eccentric loads that are large compared to their intrinsic mass.

### Isolation of Sensitive Equipment

Frequently there are requirements to isolate a piece of sensitive equipment from floor-induced vibrations. The geometry is that shown in Fig. 11.9. Since the spring supports are in their linear region the relations are the same for equipment hung from above or supported

Figure 11.9 Force Vectors of a Spring Mass System with Viscous Damping for a Moving Support

Figure 11.9 Force Vectors of a Spring Mass System with Viscous Damping for a Moving Support

Moving Support Force Vectors

Figure 11.10 Transmissibility Curves for Vibration Isolation (Ruzicka, 1971)

Figure 11.10 Transmissibility Curves for Vibration Isolation (Ruzicka, 1971)

Pn J5fn

DRIVING FREQUENCY, f

### Pn J5fn

DRIVING FREQUENCY, f from below. The transmissibility is the same as that given in Eq. 11.23. In the case of isolated equipment, instead of the force being generated by a vibrating machine, a displacement is created by the motion of the supporting foundation. In Eq. 11.23 the terms for force amplitudes are replaced by displacement amplitudes.

### Summary of the Principles of Isolation

Figure 11.10 shows the result of this analysis for both self-excited sources and sensitive receivers. The transmission equation is the same in both cases, differing only in the definition of transmissibility, which for an imposed driving force is the force ratio and for base motion is the displacement ratio. Above the resonant frequency of the spring mass system the response to the driving function decreases until, at a frequency just over 40% above resonance, the response amplitude is less than the imposed amplitude. At higher driving frequencies the response is further decreased. The lower the natural frequency of the isolator—that is, the greater its deflection under the load of the equipment—the greater the isolation.

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