120 PERIOD OF VIBRATION OF STEAM VESSELS. 



by the buoyancy gained at the ends, considering that there would be no appreci- 

 able change in trim. 



The total work would be that done in deflecting the vessel considered as a 

 beam, or, from (39), (46) and (47), in the Appendix, 



U= Wh=y2^'' Mdi +HJ'' {w-b) {v,-y)dx (3) 



and, since the two parts are equal. 



^-X 



■'■ M'dx , ^ 



WEI ^^' 



in which W represents the total weight of the vessel, or the displacement ; zv — b 

 represents the varying weight per foot run of the vessel as read from the "load" 

 curve ; and y — y is the deflection measured from the mean immersion line. 

 To obtain k'', we use the formula — 



'H 





in which w is the varying weight per foot run of the vessel as read from the weight 

 curve (not the "load" curve), and W is the total weight of the vessel. 



The value of -^ obtained for the vessel with data on Plates 56 and 57 is — 



k^ .004147 . . .^. 



T = :^i^78~ ^^^^=-3244 feet (6) 



whence 



V.P.M.=^Mdl=95.o8 (7) 



V .3244 



It will be noted that the period for the vessel shown on Plates 56 and 57, as cal- 

 culated, is about 95 vibrations per minute. This is the same vessel, however, on 

 which the vibrations were measured and found to be about 76 per minute. The 

 discrepancy indicates an error in the assumptions. At first it was thought that the 

 rigidity of a hollow riveted structure such as a vessel would be less than if it were a 

 homogeneous steel structure. This is probably true to a certain extent, and the value 

 of E to be used in the formula should be taken at somewhat less than its accepted 

 value, perhaps. Also, the value of / varies, depending on whether it is taken in 

 way of a bulkhead or between bulkheads. It is recognized also that there is a de- 

 flection of a beam due to shear action as well as to bending action. 



In addition to the preceding causes affecting the deflection, a correction 

 would be necessary on account of the fact that the value of the kinetic energy was 

 obtained by considering the weight of the vessel as the mass given motion in the 

 vibration, and the fluid effects were neglected. There is no doubt that the vertical 



