機關室の位置と船體の振動との關係

抄録

The belief, that an unbalanced force applied at the loop of the deflection curve in natural vibrations of a ship or an unbalanced moment of force applied at its node excites large vibrations under resonance, seems to have been prevalent among naval architects and engineers until recently. It appears that Schlick* was the first to give this conclusion, and the same view, being apparently established, was followed up even by some new writers such as Lewis** and Abell §.
Although I stated in a previous publication §§ that such a fact is not probable to exist from a dynamical point of view, the problem was not perfectly studied owing to certain difficulties. The present closer examination of the subject however confirms that the conception which has dominated the opinion of people is rather contradictory to nature with respect to the vibrations of a ship.
With a view to investigating the problem in the simplest possible way, I took a free-free uniform bar and calculated three cases; namely, (i) its flexural vibrations due to an unbalanced force (Appendix A), (ii) its torsional vibrations due to an unbalanced torque (Appendix B), (iii) its torsional vibrations due to an unbalanced torque moment(Appendix C). Although, in spite of its importance, the case of flexural vibrations due to an unbalanced moment of force was not studied at this juncture through some reason, it is nevertheless obvious that the nature of the problem is quite similes to the one in (iii) for torsional vibrations, and its full explanation will appear in the near future, as it is associated with some other problem.
The result of the present problem shows that, under resonance, the amplitudes of the ship's vibrations in the very vicinity of the engine room, depending on the magnitude as well as the frequency of the unbalance, either of force or of moment, besides the stiffness and the mass of the engine, are however the same wherever that engine room may be located. We also come to a conclusion that, in the case of the unbalanced force, the amplitude of a specified point in a ship in resonating forced vibrations with a given period differs in accordance with the difference in the position of the engine room, namely it is inversely proportional to such a particular amplitude that the point corresponding to the position of the engine room should have if the ship were to vibrate undamped and freely with the period under consideration Thus, should the engine room be at the node of free vibrations of the ship, the amplitudes of forced vibrations would be infinitely large, at any rate, in an idealized case, while, if the engine room were at the loop of the same free vibrations, the amplitudes of the forced ones would assume minimum values. The reverse is the case provi ed the unbalanced moment be applied in lieu of the unbalanced force.
Although accurate information is scanty now to me with respect to the details of unbalances in engines and in their accessories to cause sensible vibrations to ship structures, it seems however possible for some auxiliary engines to be more or less influential origins of the vibrations. Were such engines having unbalanced force set at a node of the principal free vibration of the ship, as will probably happen relatively frequently, excessively large vibrations of the ship's structure, particularly at the midship part as well as at its ends, would be expected.