1
Vibration Measurements Part 1
Sine Sweep Test of a Cantilever Beam
Objectives:
The objects of this experiment are to:
1.
Find the first natural frequency of a
cantilever beam using both theoretical and
experimental techniques and to estimate the first mode’s damping.
2.
Find the second natural frequency of a cantilever beam by locating its 180° phase shift.
Introduction:
Every physical bony has an infinite number of resonant or natural frequencies. The body will
vibrate with a different vibration envelope for each of these resonant frequencies. We refer to the
vibration envelope as the mode of vibration, hence we refer to the resonant frequencies as modal
frequencies. You can see the vibration envelope of a meter stick by holding it horizontally by its
end and moving it rapidly up and down. The first mode will look like a wedge with the apex at
your hand. When the meter stick reaches the edge of the vibration envelope, it must come to a
stop so it can reverse its direction. Your eye can see the stick when it briefly stops moving, but
when it passes through the midpoint it is going very fast and appears as a blur. If you shake the
stick even faster you will see the second vibration mode. No one has been able to shake it fast
enough to see the third mode
The first three vibration modes of a cantilever beam are shown in Figure 1.
Notice that each
mode adds one vibration node to the mode shape. The natural (or resonant or modal) frequency
associated with each of these vibration envelopes s greater than that associated with the previous
envelopes. That is
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2
3
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 '10
 Mysore,Ananda
 Frequency, Natural Frequency, vibration envelope

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