Vibration phenomena are caused by the following sources of excitation:

            - the propeller (periodic vibration) 

            - engine and ancillary machinery (periodic vibration) 

            - effects of the sea (random vibration)

 

Installation of ever more powerful propulsion systems on ships of high tonnage with a single driveshaft increases the discrepancy between the rigidity of the driveshaft and the flexibility of the ship’s structure. It has emerged that these phenomena have been responsible for worsening of vibration on board ships. If two sources of excitation are close in frequency, a beat phenomenon emerges, and the frequency of this beat is likely to cause a resonant response. The beat frequency is different from each of the component frequencies, is markedly lower than they are.

On ships there are structures that resonate with forced vibration, for example:

           - the entire driveshaft, which is liable to respond laterally or longitudinally to excitation from the propeller or propulsion system, and thus in turn excites the structure of the double bottom;

            - the entity made up of a diesel propulsion engine and the structure of the double bottom that supports it. This entity responds to excitation in the form of forces and moments caused by the functioning of the engine, and is likely to make the structure of the hull vibrate.

Other “passive” resonators may be excited, such as the deck, partitions, mast, radar equipment etc.

 The wake in which the propeller operates is responsible for fluctuation in the effort transmitted by the propeller to the drive shaft. It also causes fluctuations in pressure, and if cavitation occurs it increases the amplitude of fluctuations of pressure on the hull. These fluctuations of pressure are linked to the following:

            1- variations in propeller thrust: When the propeller provides thrust, the rear of each blade undergoes depression with respect to ambient pressure, and the front undergoes overpressure.

            2- the number, surface area and thickness of the blades. Pressure fluctuation is a linear function of mean blade thickness and reduces rapidly as the number of blades increases.

            3- presence of a variable pocket of water vapour on the surface of the blade and in its wake, as a result of cavitation. Cavitation is responsible for most vibration problems found on board ships, following excessive pressure fluctuations on the rear underside. Cavitation is equivalent to an increase in blade thickness, and as such causes an increase in pressure fluctuations.

The fundamental frequency of propellers is around 20 Hz for fixed-blade propellers of between 5 and 6 metres in diameter, and 10 Hz for propellers between 8 and 10 metres in diameter.

If the response frequency of the propeller blades is very high (in the audible frequency range), “singing propellers” may be heard. This can be troublesome for the crew.

Engine vibration is caused by alternating piston/crankshaft motion. Excitation caused by free forces and moments within the engine can have an effect on the vibration response of the ship’s structure and even the girder structure, particularly in medium-sized ships with 2-stroke engines.

Engines generally vibrate at between 3 and 30 Hz. 

The level of vibration depends, of course, on the type of engine, and particularly the engine speed.

 

Sea conditions can also cause several types of vibration:

 

            1- Vibration of the whole ship

The swell causes random very low frequency vibration (less than 2 Hz) of the whole ship, both longitudinally (pitching) and transversely (rolling). The frequency of this vibration is between 0.01 Hz in very calm seas and 1.5 Hz in bad weather. It is generally between 0.1 and 0.3 Hz. Acceleration ranges between 0.005 and 0.8 m/s2, sometimes reaching 1 m/s2. These values vary depending on sea conditions and the position of the subject on board the vessel [Kingma1].

This vibration causes seasickness.

 

            2- Ship girder vibrations caused by sea conditions

These are usually considered to be of two types:

  • “Whipping”, which is caused by the hydrodynamic impact to the front of the ship, and which is a transient phenomenon that causes the ship girder to vibrate.

     Whipping usually occurs when the ship is forging ahead and when there is relative movement of the stem that is great enough to cause impact:

            - “slamming”, when impact occurs to a flat part on the bottom of the ship, when it falls back to the sea after emerging.

            - “slapping”, which occurs when there are impacts on the flat surface of the stem when it has not emerged from the water.

            - large waves (“green sea”). 

  • “Springing”, which is created by excitation caused by variable hydrodynamic force created by the swell, and which is effectively a phenomenon whereby the ship’s girder is made to vibrate freely.

In conclusion: ships are environments in which significant stress is caused by vibration. Such vibration can be of very low frequency, of low frequency, and to a lesser extent high-frequency (range is between 0.01 Hz and 80 Hz, with a maximum of between 3 and 30 Hz). These vibrations can be periodic or random.

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Fig. 1  Summary diagram of vibration on board ships