LOADS ACTING ON A SHIP AND THE ELASTIC RESPONSE OF A SHIP 



309 



at sea, it is by no means common. Usually swells, or 

 waves of sufficient length to cause ship motions, are 

 covered by an endless variety of small waves, chop, and 

 ripple. These have the effect of cushioning the impact of 

 the nearly flat bottom found in most cargo ships. Theo- 

 retical efforts and model tests are suggested for the in- 

 vestigation of the impact pressure and total impact force 

 in these conditions. Theoretical work is visualized as 

 progressing in two stages: («) The impact on a single 

 sharp wave crest can be investigated and the history 

 of the force development can be expressed as a function 

 of the wave steepness; i.e., the degree of the crest 

 sharpness. (5) The results can be generalized by 

 methods of mathematical statistics to represent the 

 impact on a set of small wa\'es which are characterized 

 by the high-frequency end of a wave-energy spectnun. 



16 Evaluation of Hydrodynamic Masses for High 

 Vibration Modes is needed. The solution of the problem 

 was given initially Ity F. M. Lewis (3-1929) and J. Lock- 

 wood Taylor (3-1930&) and the ma.sses for the two 

 lowest modes were computed. The differences between 

 these two investigators were resolved, and a more com- 

 plete solution was presented by Macagno and Land- 

 weber (3-1958) together with ninuerical data for the two- 

 node vibration. The extension of this work to higher 

 modes (at least to the seventh) is visualized under the 

 project here suggested, Section 5.53. 



17 Evaluation of the Internal Damping Characteris- 

 tics of ship hulls is needed for use in the analysis of slam- 

 caused transient vibrations. The discu.ssion given in 

 Section 5.53 indicates the inaclecjuacy of the currently 

 available data. 



18 Methods of Introducing Variable (Frequency- 

 Dependent) Damping Into the Finite-Difference Com- 

 putational Solution of slam-excited vibration should be 

 developed. This is needed in order to repre.sent faith- 

 fully the transient state of the slam-excited vibration and 

 the experimentally observeil \'ariability of the apparent 

 vibration period with time. While it is not practical U> 

 distinguish among vibration modes in this method, the 

 variable damping can be set as a function of instan- 

 taneous values of dhj/dx\ d^y/dx-dt-, and d^y/dt^ as 

 shown by ecjuation (12). 



19 Active Theoretical Work in Analytical Solution of 

 Slam-Excited Vibration is Recommended, and is gi\en 

 a high priority in the present list of research topics. 

 This can be considered as a continuation of the work of 

 Ormondroyd and of Ochi, Section 5.52. Mathematical 

 difficulties so far have limited this work to the vibration 

 of beams of uniform section, considering only flexural 

 deflections. While a complete solution of the problem 

 for a true ship structure is desirable in principle, the 

 possibility of obtaining it in the near futvu'e appears to 

 be remote. However, it aj^pears to the author that a 

 simple short cut in this procedure exists and may bring 

 about a quick and comprehensive solution. It may be 

 assumed that positions of nodal points and the normal 

 mode frequencies computed for a free vibration will 



remain sensibly unchanged in a slam-caused vibration.^" 

 A number of methods now exist for the evaluation of these 

 for ship hulls (McGoldrick et al, 1953; McGoldrick, 

 1954; Csupor, 1956). These methods take into con- 

 sideration the variability of structural properties along 

 ship's length, flexural and shear deflections, and rotary 

 inertia. The activity under this proposed project can 

 be directed to evaluating the distribution f)f the momenta 

 and energies among various vibration modes. The work 

 of Ochi (1958f) in applying the method of least work 

 for this evaluation can be used as a starting point. Once 

 the energy contained in each mode (and therefore the 

 corresponding amplitude) is evaluated, the time history 

 of the entire process is obtained by a simple summation 

 of time and position dependent deflections, using appro- 

 priate added masses and damping. 



20 Experimental Measurements of Elastic Response 

 of Structures" to slam-like impact are needed for the 

 dual purpose of 1) providing the knowledge of the 

 physical beha\'ior of structures and thereby setting tar- 

 gets for the future analytical work; and 2) providing 

 experimental data for comparison with completed sec- 

 tions of analytical work. In connection with 2), struc- 

 tural tests must be plaimed for a series of structures of 

 increasing complexity. The following steps are sug- 

 gested : 



(a) Slender steel and brass bars. A uniform section 

 bar flexural theory is expected to be applicable. 



(6) A thin-walled tube (steel and brass) in the air 

 and also floating half submerged on water. A uniform- 

 bar theory leased on flexural and shear deflections is 

 expected to l)e applicable. 



(c) A built-up steel girder of uniform section and of 

 structure generally similar to those used in ships. Longi- 

 tudinal and transverse-framing types may be compared. 

 A uniform bar theory based on flexural and shear de- 

 flections and considering rotary inertia is expected to be 

 applicable with greater emphasis on shear than in sub- 

 project (b). 



(d) A complete ship model, reproducing a ship in 

 essential structural properties, such as for instance used 

 by Ochi and Sato, Sections 4.2 and 4.3. Models with 

 transverse and longitudinal framing are suggested. 



In all cases a slam-like mipact of a known force-time 

 pattern should be applied and simultaneous time history 

 of deflections at a number of points along the beam length 

 should be recorded. Suthciently close spacing of meas- 

 lU'ing points should be used to permit the comparison 

 of experimental and analytical data at higher vibration 

 modes. In steps (c) and (rf) the design of instrumenta- 

 tion should aim at distinguishing between flexural and 

 shear deflections. In all cases the impact tests should be 

 supplemented by forced-vibration tests to establish 

 elastic characteristics of structures at all vibration 

 modes. 



'" This assumption appears to be implicitly included in Ochi's 

 worli. 



"■ This project corresponds to Lewis and flerard (1958) project 

 III-3-2. 



