Page 309 - Introduction to Naval Architecture

294 VIBRATION, NOISE AND SHOCK

By approximating the value of /, Todd proposed:

Typical values of the constant in SI units with Imperial units in
parenthesis, were found to be

Large tankers (full load) 11 000 (61 000)
Small tankers (full load) 8150 (45000)
Cargo ships (60 per cent load) 9 200 (51 000)

Many other approximate formulae have been suggested. The simpler
forms are acceptable for comparing ships which are closely similar. The
designer must use the data available to obtain the best estimate of
frequency allowing for the basic parameters which control the physical
phenomenon.

Amplitudes of vibration
It has been seen that the amplitude of oscillation of a simple mass
spring combination depends upon the damping and magnification
factor. The situation for a ship is more complex. Allowance must be
made for at least the first three or four modes, superimposing the
results for each. This can be done by finite element analysis and once
the amplitude has been obtained the corresponding hull stress can be
evaluated.
The question then arises as to whether the amplitude of vibration is
acceptable. Limitations may be imposed by the reactions of humans,
equipment or by strength considerations. Sensitive equipment can be
protected by placing them on special mounts and this is done quite
extensively in warships in particular. Human beings respond mainly to
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the vertical acceleration they experience. Curves are published
indicating the combinations of frequency and displacement that are
likely to be acceptable.

Checking vibration levels
It will be appreciated by now that accurate calculation of vibration
levels is difficult. It is possible to put a check upon the levels likely to be
achieved as the ship nears structural completion by using a vibration
exciter. The exciter is simply a device for generating large vibratory
forces by rotating an out of balance weight. Placed at appropriate