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164 THE Marine REVIEW June, 1909 The Vibrations of Ships -- And the Use of a Dynamical Model for Determining the Elasticity of Ships' Part I. The Elasticity of Ships as Deduced from Experiments on the Vibra- tion of Dynamical Models. HE experiments recorded in the following pages form part of some experiments on * vibra- tions of elastic structures car- 1906-7 and 1907-8 in the Engineering Laboratory of the Naval wich, by some of the third year stu- ried out during sessions Royal College, Green- dents, The first set of experiments was un- dertaken with the view of verifying the theory of the vibration of uniform rods. A steel straight edge of rectangular section 36,11, 3.0 in. x 0.45. -in. weighing 14 Ibs. was supported at two nodes and vibrated electromagnetically, as shown diagrammatically in Fig. i The electromagnets were placed alter- nately above' and below the bar, and therefore forced it to vibrate in a definite mode; and the current to the magnets was "made" and "broken" by the vibration of the bar itself, just as in an electric bell, The frequency of vibration of the bar was measured IND i ee -------- Hic) stroboscopically, and, although several arrangements of stroboscope were used, only the final one will be described. It has the great advantage over the others that the experimenter sees at once whether the stroboscopic disc is go- _ *Read at the spring meetings of the Institu- tion of Naval Architects, March 31, 1909, By Prof. J. B. Henderson, D.Sc. ing too fast or too slow for synchron- ism, and can adjust accordingly--there- by ensuring a very high order of ac- curacy in determining the frequency. Fig. 2 shows the arrangement. The short-focus lens L, which is fixed to the vibrating bar B, forms a_ small image of the stroboscopic disc in front of the objective of the low-powered microscope M. The microscope is fo- cussed on the image of the top or bot- tom edge of the slots in the disc, The stroboscopic disc is driven by a direct current motor, and the speed of the motor is measured by a revolution counter mounted directly on the spindle. With this arrangement of stroboscope, when the disc is rotating at synchron- ous speed, i. e, one slot crossing the field of view in one period of the bar's vibration, the experimenter, on look- ing through the microscope, sees the edge of a disc whose periphery has a wavy form. If the speed of the disc is double the synchronous speed, then one sees two such discs superposed with the edge differing in phase by half a> wave length, and so on. Of course, it is necessary to exclude all direct illumination from the image of the disc. If the speed is slightly above or below synchronism, the waves ap- pear to move to right or left, accord- ing as the speed deviation is im one direction or the other, and the experi- menter has no difficulty in maintaining the same wave continuously in the field of view for five minutes at a time, if he has at his command a suf- ficiently fine adjustment on the speed of the motor. Experiments were carried out with the bar 'vibrating in its fundamental mode, and in. its: first, second, and third harmonics, nodes respectively in the length. The positions of the nodes were obtained by scattering sand on the upper sur- BIG. 2: fact, and the two supports were al- ways placed so as to coincide with two nodes. The results given in the of the experiments are following table, which With 2, -3, 4 and --§.. shows also a comparison between theory -- and experiment. Vibrations of Ships. The vibrations of the uniform bar having shown satisfactory agreement between theory and experiment, and the. apparatus being ready for the study of the vibrations of any elastic structure, it was decided to obtain the periods of vibration of a ship by means of her dynamic model, as was done by 'Mr. A. Mallock. By a dynamic model is meant a beam or girder which has a load curve similar to the load curve of the ship, and a curve of moments of inertia of sections about the neutral axes similar to the corresponding curve Frequency of Distance of nodes from vibration. nearer end, measured 'Complete peri- in 'fractions' of the ods per second. length. Re _ 3 ¢ § Se a Rf ¢ : ° vo 9° Oo 5 a H a a & cl ey BH 2 225 72.3) 0.224 0.2242 3 200 201° .0.130;.0.5 0;14321;.0; 4 394 394 380.094, 0.358 0.0944, 0.3558 5 649 651. 0.073, 0.277, 0.5 0:0735;-0.27720:5 for the ship. The scale for the load curve does not require to be the same as the scale for the moment of inertia curve. The period of vibration of a beam will depend on the stiffness of the beam in bending, on the mass of unit length, and on the length of the beam. Hence, if we know the periods of both ship and model, we can deduce the elastic properties of the ship; or, we can calculate the period of the ship from that of the model. H. M. S. Pathfinder was chosen, for which the curve of weights had been worked out with great accuracy and for which the curve of moments of in- ertia of a number of different sections had also been calculated. She is a scout of about 3,000 tons displacement. The condition of lading corresponded to the bunkers being about half full of coal. A dynamic model of the ship was made from a bar of steel of uniform thickness, 48 in. long, 34 in. thick, the breadth being varied so as to give the correct relative moment of inertia for every section. Since the moment of in- ertia of the section is simply propor-