Page 471 - Industrial Power Engineering and Applications Handbook

Testing of metal-enclosed switchgear assemblies 141445
the inhabitants in the vicinity. Such tests are advisable The amplitudes of oscillations will depend upon weight,
even for machines, devices and components that are to stiffness and configuration. The record of these
be installed in other critical areas, such as a refinery, a oscillations is known as free vibration record. The rate
petrochemical project. handling and filling areas of of oscillations will determine the natural frequency of
inflammable liquid, gas or vapour where also as a result the object. Figure 14.20 shows one such free vibration
of failure of such machines system process or control record.
may be jeopardized and cause serious accidents, and
resulting in heavy loss of life and property. The seismic Damping is the characteristic of a vibrating system
worthiness relate more to the primary system than to the which defines how fast the amplitudes of a freely vibrating
secondary. For a secondary system, it applies only to system will decay. The greater the damping of a system,
\afety-related equipment or devices installed in critical the faster the amplitude will decay and vice-versa. The
areas as noted above. The suitability of primary systems magnification of vibrations of a system, as a result of
is verified through analytical means only, as laboratory ground movements, will depend upon its natural frequency
test for such systems are not practicable. and level of damping.
Hydro projects, dams, bridges. naval equipment and Generally, all systems are flexible to some extent, except
any installations that are prone to continuous shocks and a few that may be completely rigid. A flexible system
vibrations also require their primary and secondary can be represented as shown in Figure 14.21, where
systems to have a better design and operational ability to ‘resistance’ represents the restoring force developed within
withstand seismic effects or other ground/surface vibra- the system, when applied with a force to displace it from
tions. No specific tests are presently prescribed for such its original axis X-X‘. It will try to regain its original
applications. But response spectra can be established even shape and position and vibrate about its axis until it
for such locations and the primary and secondary systems attenuates due to damping. Vibrations are caused as the
annlysed mathematically or laboratory tested. system (which may be any object) returns to its original
We define below some common terms in earthquake position and overshoots the original axis X-X’ to the other
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engineering to clarify test requirements and methods: side. Thus vibrations of the system about its axis,
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commence until they attenuate. The ‘dashpot’ represents
Ground acceleration This is the time history of the resilient characteristic of the body that would try to
ground acceleration as a result of an earthquake, where damp the oscillations thus developed and attenuate it.
inultiple frequency excitation predominates (Figure The following mathematical expressions derive the pro-
14.12(b). A ground response spectrum (GRS) can be perties of a system when excited by an external force
derived from this history. F,,,:
Floor acceleration This is the time history of
acceleration of a particular floor or structure caused F([) = mx” + cx’ + kx
by a given ground acceleration (Figure 14.16). It may
have an amplified narrow band spectrum due to where
structural filtration, where single frequency excitation F,,, = force applied to the object as a function of time
and resonance may predominate. depending upon the x = displacement of the object
dynamic characteristics of the structure. A floor response x‘= velocity of the mass attained when affected by
vibrations
yectrum (FRS), as shown in Figure 14.18, can be x’’ = acceleration of the mass attainccl during the course
derived from this history. Consideration of GRS or
FRS will depend upon the location of the object under of restoring force.
te\t. ni = mass of the object
Broad band This means multiple frequencies of c = coefficient of viscous damping
ground movements. During an earthquake these assume K = coefficient of restoring force (or stiffness of the
multi-frequency characteristics, which are represented foundation)
by broad band response spectra (Figure 14.13). When, This equation can also be rewritten as
however. such a response is transmitted to secondary
k
systems and objects mounted on floors, it becomes a 32 - xJf+ L-.x’+ - .x
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narrow band, due to floor and structural filtration, and tn rn m
the amplitude of vibration is magnified. The If w, is the natural angular frequency of vibration of an
magnification will depend upon the natural frequency object in rad/s, Le. 2~;fheing the natural frequency of
and damping of the secondary systems and the objects. vibration in Hz, then
As normal practice, all systems and objects, mounted
on the ground or a floor, must undergo multi-frequency 0, = -V’; Ik
tests. The shake table is excited to achieve a movement = 2nf
that represents a broad band waveform which will
include all frequencies in the range of 1-33 Hz.
Natural frequency When an object is mounted in
situ (as in normal operation) and given an initial external
displacement or velocity in any direction and then Since the natural time for one full vibration (one cyclc),
released, the body will oscillate about its initial position 1
in a sinusoidal waveform as illustrated in Figure 14.20. T= 7