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Machinery such as engines, fans, electrical motors, compressors etc.
can constitute important sources for both air-borne and structure-borne sound (vibrations). Other equipment might be sensitive
to vibration excitation. Vibration isolation or as it is also referred to ‘resilient mounting’ can be used to
achieve significant reductions of transmitted vibrations. Figure 1 shows to the left a diesel engine hard mounted resulting
in a vibration level, v’f , on the foundation and the
same system to the right with a resilient mounting resulting in a vibration level vf
on the foundation. The effectiveness of the vibration isolation is given by its insertion loss in dB: IL = 20 log10 (v’f/vf).
There exist many types of vibration isolators. These can roughly be divided into three groups i.e. those
based on steel springs, on rubber, and steel cushions (see Figure 2). The choice of the most suited vibration isolator is
problematic. Frequently, the choice is based on only on the manufacturer’s specifications i.e. physical dimensions
and estimated natural frequency for a given mass loading. The natural frequency is normally calculated from the simple single
degree of freedom system shown in Figure 3 consisting of a mass connected to a perfectly rigid foundation via a spring and
a damper. Based on this system the force transmissibility, T = Ff / Fm, can be determined. Figure 4 shows a plot of the force
transmissibility, T, as a function of the frequency normalised with the
natural frequency of the elastic mount, f0. Two important facts
can be seen from Figure 4. First, it can been seen that the resilient mount only provides vibration isolation for frequencies
higher than 1.4 f0. Secondly while some damping, here given
by the critical damping ratio ζ, is good for controlling the response
at the natural frequency too much damping will have a detrimental effect on the vibration isolation at higher frequencies.
For real systems, the foundation will not be perfectly rigid as in Figure 3 and a more complex model is required to
accurately describe the engine – isolator – foundation system. Figure 5 shows a model where the vibration isolator
is described by a passive four-pole. The properties of the engine foundation and the base of the engine are described by their
complex mobilities (velocity/force). The vibrational source strength of the engine is here modelled as a velocity source.
Analysis of the system in Figure 5 gives that the previously mentioned insertion loss can be found as IL=20 log |A+C/(Mm+Mf)|
where A is 1 for a perfectly mass less spring and C=vm/Ff. The important conclusion is that a high insertion loss, IL, requires that not only should the vibration isolator be very soft but that the mounts for the
isolator should have very low mobility i.e. be very stiff.
Figure 6 shows a comparison between a measured
steel spring and a rubber cushion. The data has been normalised so that both isolators have the same static deflection. The
data shows that at the lower frequencies the steel spring has the lowest transmissibility. However, at higher frequencies
the transmissibility of the steel spring deteriorates due to standing waves (seen as peaks). The rubber cushion is not affected
by standing waves as the rubber is highly damped.
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