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



305 



calculations of motions. Basing tlie entire investiga- 

 tion on calculations can be expected to yield more con- 

 sistent results from which it will be easier to derive 

 various trends. Unlike the bottom impact of cargo 

 ships, the force acting on a submerged destroyer bow 

 consists of the static buoyancy and of dynamic pressure 

 forces of the same order of magnitude. The measure- 

 ments of the time history of the hydrodynamic force 

 during flared bow submergence is also recommended. 

 This can be done on models in towing tanks. Care must 

 be taken to consider the hydrodynamic force and not the 

 model's elastic I'esponse. The latter appears to differ 

 from the response of a full-size ship. 



8.7 A Ship's Elastic Response. By far the most 

 neglected -Mid most needed liekl of research in ship 

 stresses lies in the determination of a ship's elastic re- 

 sponse to a slamming impact. This subject was out- 

 lined in Section 5.5. The importance of it was demon- 

 strated bv the preliminary data on tlestroyer tests puh- 

 hshed l)y Warnsinck anil St. Denis (3-"l957, NSMH 

 Symp.). In these tests the bending stress amidships 

 was more than doubled by the slamming impact.''''* 

 The important feature of the impact action is the fact 

 that the critical stress docs not occur at the time of im- 

 pact but some time later. The first cff(>ct ui the impact 

 is to excite ship vibrations of all modes. The supei- 

 position of several modes of vibration defines the tran- 

 sient state. During the transient state, the initial peak 

 hogging bending moment at the point of an imjjact 

 gradually but rapidly changes to the peak alternating 

 hogging-sagging moment slightly forward of amidships. 

 This is associated with a two-node mode of vibration. 

 In the transient process, dangerous peaks of stress may 

 occur at structural discontinuities and also at discon- 

 tinuities of mass distribution. The bending stress of the 

 two-node vibration is superposed o^'er the maxima (jf 

 several bending-moment cycles which occur at the fre- 

 quency of wave encounter. Not only the maximum 

 stress is often more than douliled but also a large niun- 

 ber of stress fluctuations is thereby produced. 



8.71 Suggested procedure in research on elastic 

 response. As has been stated already, the research 

 in the elastic response of ships appears to be in 

 its infancy. Very few references were found in the 

 literature and these were mentioned in Section 5.5. 

 These references had given a rather incomplete treat- 

 ment of an impact on a slender beam and have not yet 

 considered a complete ship structure. In its entirety, 

 the problem is evidently extremely complicated. In 

 order to formulate a fruitful research and to make rapid 

 progress, it is necessary to subdivide it in its composite 

 parts. 



It appears to the author that it is possible in the first 

 approximation to separate the impact investigations 

 from the investigations of the vibratory characteristics of 

 ships. A laige fiterature already exists in regard to the 



latter. 5^ It deals with free vibrations and with the 

 steady-state forced harmonic vibrations. The most 

 important results of investigations are the evaluation of 

 the locations of nodal points and of frecjuency of dif- 

 ferent vibration modes. Next in importance, and ap- 

 parently less developed, is the experimental evaluation of 

 damping characteristics for different modes. The deter- 

 mination of these characteristics for higher modes is 

 important in evaluating the transient vibration after 

 impact. 



An analysis of the impact response can be simplified by 

 assuming the location of the nodal points and of fre- 

 quencies of vibration as they are found from the afore- 

 mentioned analysis of harmonic-vibration characteris- 

 tics. The analysis of an impact response can then be 

 made assimiing the structure to be an artificial simple 

 slender beam limited to the modes of vibration described. 

 The problem is reduced to finding the amplitude of each 

 mode of vibration as a function of an impulse Pt and its 

 location with respect to the locations of nodal points. 



It is believed that the simplest form of solution will be 

 obtained with a rectangular impulse of a localized uni- 

 form force P acting over an extremely short time r. A 

 certain distribution of impulses along a ship's length will 

 be necessary in order to represent a pressure area of a 

 given magnitude. For the more slowly applied impacts 

 of flared bows, such as are found in destroyers, an ad- 

 ditional distribution of impacts with time will be neces- 

 sary. 



In the form of research suggested above the problem 

 is subdivided in four stages: 



1 Determination of frequencies and locations of nodal 

 points for a number of vibrational modes. An evaluation 

 of the corresponding damping characteristics (by analysis 

 of experiments). 



2 Distribution of amplitudes excited in all significant 

 modes by a single impulse. A simple beam theory is 

 used, but the beam is artificial in that it is limited to the 

 vibration characteristics found under (1): 



3 After completion of the foregoing solution, the 

 transient time history of deflection and stresses can be 

 computed readily by simple summation of deflections 

 caused by all vibratory modes along the entire length of a 

 ship. 



■1 Superposition of deflections caused by impulses 

 distributed along a ship's length and with time in order 

 to represent an actual force distribution. 



Some readers may not agree with the simplifying order 

 of procedure suggested and may formulate another ap- 

 proach. The author only wishes to emphasize the 

 importance of the research in this field and the need to 

 simplify the complicated problem. It appears to him 

 that a principle "to divide and to conquer" is a promising 

 approach, which moreover, permits spreading the work 

 among many investigators. Apart from the funda- 



™ Previous data were obtained on slow cargo ships and indicated 

 bending moment increases of tlie order of 20 per cent. 



'' The investigation of a ship's structural characteristics is out- 

 side the sco]je of the present monograph. The following two refer- 

 ences can be given, however, as illustrating the latest achievements 

 in this field: Mctloldrick and Russo (1955) and Csupor (1956). 



