Page 295 - Introduction to Naval Architecture

280 VIBRATION, NOISE AND SHOCK

Irregular forcing function
In the above the forcing function was assumed sinusoidal and of
constant amplitude. The more general case would be a force varying in
an irregular way. In this case the force can be analysed to obtain its
constituent regular components as was done for the waves in an
irregular sea. The vibratory response of the system to the irregular
force can then be taken as the sum of its responses to all the regular
components.

SHIP VIBRATION

The disturbing forces
A ship is an elastic structure and will vibrate when subject to oscillating
forces. The forces may arise from within the ship or be imposed upon
it by external factors. Of the former type the unbalanced forces in main
and auxiliary machinery can be important Rotating machinery such as
turbines and electric motors generally produce forces which are of low
magnitude and relatively high frequency. Reciprocating machinery on
the other hand produces larger magnitude forces of lower frequency.
Large main propulsion diesels are likely to pose the most serious
problems particularly where, probably for economic reasons, 4 or 5
cylinder engines are chosen. These can have large unbalance forces at
frequencies equal to the product of the running speed and number of
cylinders. These forces can be at frequencies of the same order as those
of the hull vibrations. Thus quite severe vibration can occur unless the
engines are very well balanced. Auxiliary diesels tend to run at higher
speeds. Their frequencies are higher and may excite local vibrations.
Vibration forces transmitted to the ship's structure can be much
reduced by flexible mounting systems. In more critical cases vibration
neutralizes can be fitted in the form of sprung and damped weights
which absorb energy or active systems can be used which generate
forces equal but in anti-phase to the disturbing forces.
Misalignment of shafts and propeller imbalance can cause forces at a
frequency equal to the shaft revolutions. With modern production
methods the forces involved should be small. A propeller operates in a
non-uniform flow and is subject to forces varying at blade rate
frequency, that is the product of the shaft revolutions and the number
of blades. These are unlikely to be of concern unless there is resonance
with the shafting system or ship structure. Even in uniform flow a
propulsor induces pressure variations in the surrounding water and on
the ship's hull in the vicinity. The variations are more pronounced in
non-uniform flow particularly if cavitation occurs. Stable cavitation over