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June, 1909 tional to the breadth, it is sufficient to make the breadth directly proportional to the ordinates of the moment of in- ertia curve, in order to have the beam to scale as regards the stiffness. The scale of loads is then fixed by the sec- tion which has minimum ratio of load to moment of inertia, since at this sec- tion we want the weight of the bar itself to represent the load, and at all other sections we can add lead weights to bring up the mass of unit length to the corresponding amount on the ship. Thirty lead weights were neces- sary to bring the loads to correspond with the load curve of the ship, and these were soldered to the bar. It was anticipated that soldering these masses of lead over a considerable portion of the length of the bar would stiffen it considerably; but experiments made with the lead continuous, and also with it cut up into .very short lengths, showed no marked alteration in the period of vibration. Hence the lead cannot contribute to the stiffness to any appreciable extent. The scale of weights was found by weighing the finished model, and the position of the center of gravity of the model was found to be less than 0.25 per cent of the length of the model from the correct position as calculated an the ship. In order to force the bar to vibrate by means of electro-magnets placed al- -ternately above and below the _ bar, the lead weights had to be soldered at some parts of the length above the bar, and at other parts below it, so that the magnetic pull might come di- rectly on the bar with as small an air gap as possible, and with no lead be- tween the magnets and the bar. Suf- ficient vibration was always obtainable to determine the nodes, whether the supports were near. or far from them; but, in the determination of the fre- quency, the supports were always moved so as to coincide with two nodes. Experiments were carried out with the model vibrating with two and also with three nodes in the length, and the results are given in the following table: VIBRATION OF THIE DYNAMIC MODEL OF H. M. S. PATHFINDER. Frequency--Com- Pos'tions of nodes in No. of plete periods fractions of the length nodes. per second. from the bow. 2 81.8 0.280, 0.728 3 194 0.179, 0.515, 0.832 The frequency of the model with three nodes is 19 per cent greater than double the frequency with two nodes, but 1414 per cent less than it would be if the periods followed the same law as in the uniform. bar. If the modulus of elasticity of the ship were equal to the modulus of the 'TAE. MarRINE. REVIEW bar, the scales of the ship and model are such that the frequency of the ship would be 127 per minute. Un- fortunately no pallograph records are available for this ship, but I am indebt- ed to the Admiralty and to the officers of the ship for carrying out some ex- periments on her vertical vibrations, They report that the frequency of ver- tical vibration is 106 per minute when the engines are running at 100 R. P.M. Hence the modulus of. the ship must be less than that of the model in the 106 & i. e., 30 per cent lower. ratio: = 0.70 Vibration of Turbine Steamer. The first set of experiments having been carried out on the model of a gun-boat, it seemed desirable to repeat the experiments with another type of ship, and preferably with one whose pe- riod of vibration had been accurately determined. The writer is very much indebted to Messrs. John Brown & Co., and the joint managing directors, Messrs. :Chas. -E. Ellis aud, J.:G;.Dun- lop, for the data regarding the turbine steamer Lusitania which enabled her model .to be constructed, and also for the pallograph records of her vibra- tions at sea. The dynamical model was made 48 in. long, 34 in. thick, and with a maximum breadth 5.1 in. The results of the experiments are as_ follows: . brations, VIBRATIONS OF MODEL OF TURBINE STEAMER. Positions of nodes No. of Frequency from bow in fractions nodes. periods per second. of the length. a "72.05 0:26, 0.76 3 182 0.153, 0.53, .0.853 4 350 The frequency of the model, accord- ing to the scales chosen, should be 584 times the frequency of the ship. Hence for equal moduli the fundamental fre- quency of the ship should be: 725 1.244 74.6 58.4 sec. min. The actual frequency of . the sh"p is 65 per minute; hence the ratio of the elasticity of the ship to that of the model is: (-- ae 74.6 or the elasticity of the ship is 24 per cent less than that of the model. This is greater than was obtained for the Pathfinder, but the plating in the scout is very much thinner than that in the liner. Thin plates are, as a rule, more buckled than thick plates; and,. since the buckles straighten out when a pull stress comes on them, the 'Pathfinder. 165 thin plates must give a lower modulus in vibration than the thick plates, be- cause, when a plate straightens under pull stress, it is equivalent to an in- crease of strain for the same stress. An objection may be raised against the comparison of 'ship and model in that the model vibrates freely in air, while the ship vibrates in water, and has its vibration considerably damped. We are dealing, however, with the forced vibrations of the ship, due to a periodically applied force arising from rotation of the screws or other ma- chinery on board, and such forced vi- when damped, always reach their maximum amplitude if the pe- riodicity of the exciting disturbance agrees with the natural free period of the vibrating structure, In ships the amplitude of vibration iS, ae a -pule, negligible, unless there is approximate equality in the period, In addition to its damping effect on the vibrations the water has another effect, especially when the period of vibration is very slow, for then the water will move in stream-line motion backwards and forwards along the bot- tom past the nodes, as one portion of the ship rises and the neighboring por- tion sinks. The more rapid the vi- bration the less must this effect be. Experiments show that the virtual mass of a body rotating in a fluid is very much less than the virtual mass of the same body moving through the fluid, and we would anticipate that the virtual mass in vibration would be -still less" than in rotation. It is important to re- member that this effect is present, al- though: of small magnitude, and that it would probably have no greater in- fluence than the quantities which are neglected or allowed for roughly in the calculation of the moments of in- ertia of the ship. In. calculating the moments of inertia the practice is to neglect the wooden decks or sometimes to add 1-25 of their thickness to the steel decks below them. This was done in the case of the In strength calculations the wood of the deck would only contribute to the strength of the ship in sagging, and not in hogging; but in vibration it would always contribute to the stiff- ness, since the fastening between wood- en and steel decks is quite sufficiently strong to take the small shear stresses introduced by the vibration. It is also customary to neglect the intercostal girders in calculating the moments of inertia. These girders may not con- tribute much strength to the weakest sections of the ship, but they certain- ly contribute to the stiffness of the ship as an elastic structure.