142 ON VIBRATIONS OF BEAMS OF VARIABLE CROSS-SECTION. 



in a paper contributed to the Institution of Naval Architects by Dr. Giimbel, who there gives 

 further references to similar work in French and German publications. 



It is of great interest to hear from Commander McEntee how this method has been veri- 

 fied by experience in our Navy. 



The following list of references may prove useful. 



From our own Transactions: — "Balancing of Marine Engines"; 1901, Rear Admirals 

 D. W. Taylor and G. W. Melville, U. S. N. "Vibration of Steamships" ; 1902, Rear Ad- 

 miral G. W. Melville, U. S. N. "Period of Vibration of Steam- Vessels"; 1915, W. Gate- 

 wood. 



From the Institution of Naval Architects, London : — "Torsional Vibration of Shafts" ; 

 1902, Dr. L. Giimbel. "Our Present Knowledge of the Vibration Phenomena of Steamers" ; 

 1911, Dr. O. Schlick. "Torsional Vibrations of Elastic Shafts of Any Cross-section and 

 Mass Distribution, and Their Application to the Vibration of Ships" ; 1912, Dr. L. Giimbel, 

 "Some Experiments on the Influence of Running Balance of Propellers on the Vibration of 

 Ships"; 1917, J. J. King-Salter, R. C. N. C. 



Captain W. Hovgaard, Member (Communicated) : — -Mr. Akimoff's paper is of great 

 value to the profession, as it affords an excellent introduction to the problem of vibrations, 

 giving a comprehensive and yet brief view of the present status of the science. His exposition 

 of Ritz's method is of great interest in that it enables the naval architect to deal in a relatively 

 simple manner with the most complex problems that are likely to occur in the study of deflec- 

 tions and vibrations of ships. 



In the discussion of the principle of virtual work, Mr. Akimoff refers to the problem of 

 finding the elastic line for a ship in dock. This is a subject to which I have given consider- 

 able study, and my general impression is that when a ship is' well supported it does not, 

 except for the overhanging parts at the ends, take any appreciable deflection as a girder. It 

 behaves more as a limber body with rather insignificant deflections determined chiefly by the 

 local distribution of the weights in the ship and of the keel blocks. Thus points of increased 

 compression of the blocks are likely to be found at each of the main transverse bulkheads. 

 This remark applies in particular to large vessels and where the total area and distribution 

 of the blocks are in accordance with good practice. The deflection of the overhanging ends 

 may be considerable, but will rarely cause excessive general strains in the structure. The 

 deflection of such parts can, of course, be determined graphically by the theory of bending. 



It would be of interest to know more definitely what Mr. Akimoff means by "plain static 

 and dynamic unbalance" to which, on the last page of the paper, he ascribes vibrations. 1 

 confess I belong to those who believe that vibrations are due chieily to the action of the en- 

 gines and the propellers. 



Commander J. J. Manning, U. S. N. (Communicated) : — On a ship at sea, steaming 

 at normal speed, I have noticed in some cases very little vibration up to a certain point. At 

 this point, termed "critical speed," which I have noticed, while standing watch on the bridge 

 (located one-half the distance between the center, or amidship section, and the bow), the 

 vibration is excessive, having an amplitude, I should judge, anywhere from one-half inch to 



one inch. 



One particular instance I recall. While officer on the bridge at sea, on one of our battle- 

 ships in fleet formation, we suddenly lost one blade of our starboard propeller. We were 



