Natural frequencies of free vertical ship vibrations 1

The present investigation deals with some problems in the calculation of ship-hull vibrations. For practical purposes only the determination of natural frequencies of free vertical vibrations is considered.

Especially one assumption, that the influence of the mass-moment of inertia is negligible, is investigated. Therefore a number of computation-methods is considered on their possibility of taking that influence into account.

Two methods appear to be useful:

(1) the Holzer-Myklestad method (Prohl’s method);

(2) a method using influence functions, that has not yet been applied to ship vibration.

Computations with these two methods were carried out on an electronic computer for three cases: a uniform beam, the SS. “Gopher Mariner” and the MS. “Naess Falcon”. This made clear that the Holzer-Myklestacl method requires a division of the ship into about 60 elements to obtain a reasonable accuracy. The method of influence functions gives satisfactory results when using only 20 elements.

For the MS. “Naess Falcon” computations were carried out, both taking the influence of the mass-moment of inertia into account and neglecting it. There was no significant difference between the results of these cases, so that the neglection is permitted.

Besides, as could be expected, it was found that beyond the fourth or fifth mode the approximation of the ship-hull by a “Timoshenko-beam” is no longer justified.