PERIOD OF VIBRATION OF STEAM VESSELS. 121 



motion of any part of the vessel is accompanied by a motion of the adjacent water, 

 and that the mass given motion is really greater than was assumed. But none of 

 these corrections seem sufficient to account for the discrepancy. 



The vessel was considered as a beam with loads concentrated along the neu- 

 tral axis. Actually, the depth of the vessel is about one-twelfth of the length, and 

 the loads are distributed throughout the depth of the vessel. Some of the weight, 

 indeed, is at quite a distance from the neutral axis. If the vessel were a beam sup- 

 ported at the ends, this would not introduce a very serious error into the calcula- 

 tions. But when the points of support are near the quarter-length of the vessel, 

 the relative effect is greatly increased, as so much of the weight has fore-and-aft 

 motion during the vibration, with no appreciable vertical movement. It is consid- 

 ered that the effect of taking into account in the calculations the vertical distribu- 



tion of the weights on the vessel will be to increase the value of -^ about 56 per 







cent, and to decrease the number of vibrations per minute from 95 to about 76, the 

 observed value. 



If the vessel in question is typical, the number of vibrations per minute as 

 calculated, without allowing for the vertical distribution of the weights, would need 

 to be reduced by about 20 per cent to obtain the actual figure. 



When a beam vibrates, the reactions at the supports are affected. The prob- 

 able effect in the case of a vessel with deflection curve as shown on Plate 57 may be 

 obtained by considering that the reactions are least when the beam has least flex- 

 ure, and the reactions are greatest when the beam has maximum flexure, and in 

 each case correspond to the steady condition which would produce the flexure. By 

 analogy from the "Rod in Tension," considered in the Appendix, the weight (in 

 this case the vessel as a whole) will be at its top position when the unbalanced 

 force tending to lower the weight is greatest, and at its bottom position when the 

 force tending to raise the weight is greatest. In the case of the vessel, the draft 

 will be least when the flexure is greatest, and the draft will be greatest when the 

 flexure is least. 



The amount of the dipping motion as determined in the Appendix, considering 

 the amplitude of the vibration as one-tenth of the deflection in each direction, 

 amounts to .00678 foot. Plate 58 shows this forced "dipping" motion combined with 

 an assumed amplitude of vibration of one-tenth of the deflection, and from this it 

 appears that the effect is to cause the nodes to approach each other, to reduce the 

 vertical motion amidships, and to increase the motion at the ends. 



The nodal points as observed on the vessel are marked on Plate 58, but no spe- 

 cial means were used to locate them accurately. 



Attention is invited to the fact that in shoal water, on the vessel observed, vi- 

 bration seems to start at about six revolutions per minute less than it starts in deep 

 water. No explanation is apparent. 



It will be noted that ^ for any vessel considered as a beam is a function of 



o 



