A Contribution to the Vibration at the Stern of Single Screw Vessels

Abstract

The questions to the vibration at the stern of single screw vessels has recently become serious.
That behaviour is original and anomalous compared with the normal type of transverse vibration on ships.
There is increasing vibration amplitude in the after-quarter of the ship, with very little or no vibration noticeable on the hull forward of the after-quarter point.
The maximum vibration occures at the stern of the ship.
The distribution of amplitude along the hull is shown roughly in Fig. 1.
Professor L. A. Baier published his observation and its solution how he had eliminated the vibration at the stern in Trans. of S.N.A.M.E., 1952, Vol. 6.
The author observed similar phenomena on several oil-tankers on service, and found a fact that some parts of engine (including H.P. and L.P. turbine, condenser, reduction gears, piping and etc.) also vibrated transversely.
The frequency of hull and engine is nearly equal to number of blades of propeller×r.p.m. of shaft.
So, the author studied them theoretically in view of the coupled oscillation concerned with hull and engine, and forced by the unbalanced power of propeller.
Fig. 2 & 3 Rough arrangements of hull and engine.
Fig. 4 Whole system corresponding to hull and engine.
Fig. 5 Distribution of force generated by propeller and reaction of engine.
Fig. 6 Diagram of frequency equation-(35).
Fig. 7 Amplitude of several points along the hull; result of equation-(43).
Fig. 8 The modes of hull under forced vibration by propeller ; the eighth mode shows the vibration at the stern.
Fig. 9 Varions type of the vibration at the stern based on forced frequency and stiffness of engine.