294 



THEORY OF SEAKEEPING 



43 Comparison of experimental and theoretical values of superimposed stress on deck amidship; V-form 



model (from Ochi, 1958) 



equation (V.i) fur a flexural deflectidii of a bar of uiiiforni 

 section assuming a constant value of the coefficient of 

 accession to inertia. In this connection he represented 

 the damping cocfhcient b as 





(14) 



The resultant partial differential e(|iiation is identical 

 with equation (12) if the terms connected with shear 

 deflection and damping are omitted. Ochi (1958f) 

 obtained the solutions for two phases of the vibration 

 process, < t < t and t > r, where r is the diu'ation of 

 the impact force. The solution for the deflection and 

 bending stress was given as the sum of deflec^tions and 

 stresses in various \dbration modes and the investigation 

 was carried up to the seventh mode. A novel and par- 

 ticularly important part of this work is the evaluation 

 of the impact-momentum distriliution among various 

 modes by the least-work analysis. The damping was 

 taken as a function of the vibration freciuency; i.e., 

 was different for each mode. 



Ochi made computations for a l)ar with structural 

 properties corresponding to the brass ship moilel which 

 he had tested in a t(nving tank. The comparison of the 

 computed and experimental vibration response to a 

 slam is shown in Fig. 43. The agreement is shown to be 

 good except in the hrst vibration cycle. Conceivably, 

 at the first instant the impact momentum is primarily 

 al)sorbed in shear deflection and the neglect of this in 

 computations led to the incorrect evaluation of the 

 first vibration cycle. A satisfactory agreement in the 

 subse(iuent cycles can be interpreted as a confirmation 



" In foot-tons for a full-size ship. 



of Ochi's impact-momentum distribution among vibra- 

 tion modes and of his damping estimates. On the other 

 hand, the results can be taken as fortuitous since neither 

 shear deflections nor the variation of the mass and struc- 

 tural properties along the length of the ship were taken 

 into account. 



A contribution of the imp;ict momentum to a partic- 

 ular vibration mode depends on the location of the im- 

 pacting force with respect to nodal points of the elastic 

 curve. Therefore, the distribution of a concentrated 

 impact among various modes varies rapidly with the 

 location of the impact. In reality the impact force is 

 always distributed over a certain bottom area near a 

 ship's bow. Ochi (1957, 1958a) measured the pressure 

 distribution during model slams in a towing tank and 

 approximated this distribution in the vibration analysis 

 by five localizeil forces. The resultant contributions of 

 various modes to the bending moment amidships is shown 

 in Table 10. 



It should be noted that contributions of even modes 



