310 



THEORY OF SEAKEEPING 



Direct objectives of the tests are to pl•o^•ide data for 

 comparison with analytical work, to evaluate internal 

 damping/- and, in structures alternatelj' tested while 

 floating on water, to e\'aluate added masses. 



In tests made in the air a free-free condition may be 

 achie\-ed b.y suspending a structiu'e on a number of light- 

 weight long springs of low spring constant. 



21 Investigation and Well-Defined Statement of 

 Similarity Relationships should be developed for ships 

 and models involving hydrodynamic loading and the 

 elastic response of the structure, Section 5.54. It 

 appears at the moment that the strong dependence of 

 the structural damping (hysteresis) on A'ibration fre- 

 quency prevents direct comparison of models and full- 

 size ships. It is necessary to establish what information 

 can be obtained in model tests and how it should be 

 interpreted to indicate the ship behavior. The investiga- 

 tion suggested here also has bearing on the compariso«i 

 of sea-observation data obtained on ships of different 

 sizes and types. 



22 Parallel Investigation of Transient Elastic Vibra- 

 tions on a Ship and a Model is suggested. For tliis pur- 

 pose the model listed in project 20 item (d) should cor- 

 respond to an available ship. Also the model test con- 

 ditions should include those practical for the ship, such 

 for instance, as the dropping of an anchor. The sup- 

 plementary steady-state vibration tests on the model 

 should be produced in a manner similar to those pro- 

 duced by the vibrator available for the ship. 



23 Detailed Step-by-Step Calculation of Forces Act- 

 ing on a High-Speed Ship Model and the Resultant 

 Model Vibrations is recommended as a further de\'elop- 

 ment of the pioneering attempt by Dalzell, 1959, Section 

 5.55. It is suggested that such investigation be made on 

 a destroyer model in an irregular sea imitating the con- 

 dition reported by Warnsinck and St. Denis (1957). A 

 short sample of a wave record can be chosen starting 

 with a ciuiescent period and running through a group of 

 high waves. Corresponding ship motions can be esti- 

 mated by the linear theory of Fuchs and McCamy 

 (3-1953). Such a project will help to develop under- 

 standing of the wave and slam-e.xcited vibration of 

 destroyers. 



24 Statistical Collection of Bending-Moment Data 

 Related to Sea Conditions is recommended. This is to 

 be a continuation and further development of E. V. 

 Lewis' activity described in Section 6. It is suggested 

 that the weather log as well as the deck log be used in 

 reporting sea conditions. It is also suggested that ships 

 be equipped by two strain gages, one on the port and one 

 on the starboard sides, since unusuall_y high stresses 

 conceivably may be caused by the rolling of the ships 

 (with excessive metacentric height) in head seas. There- 

 fore, the amount of rolling should be recorded, or at least 

 commented upon. 



'- The evaluation of internal dam])ing is emphasized by Lewis 

 and Gerard (1958) in their suggested project III-3-4. 



25 Development of a Statistical Method for Predic- 

 tion of Wave Steepness in a Specified Wave Length 

 and in Specified Wave-Energy Spectrum is recom- 

 mended. This is needed in connection with establishing 

 the maximum bending moment expected in ships at sea. 

 A rather high priority is suggested for this project. 



26 Effect of Discontinuities on the Elastic Response 

 should be investigated by experimental and analytic 

 means. The experimental data should be obtained to 

 establish the pattern of physical events. A suitable 

 mathematical model can be formulated after examination 

 of this pattern. On the other hanci, analytical work can 

 be pursued concurrently with the particular aim of 

 checking whether the existing vibration theories will 

 yield satisfactory results by mere insertion of discon- 

 tinuous mass and structural property distributions. It 

 is emphasized that discontinuities in mass as well as sec- 

 tional property distrilnitions are important. 



27 Experimental Investigation of the Impact of 

 Prismatic and Cylindrical Bodies^' of the section tj'pical 

 of bow sections of ships is suggested in order to help the 

 anah'sis of pressure and forces experienced by ships in 

 slamming impact. Two distinct ca.ses are visualized here. 

 In sections typical for cargo ships the deadrise angle is 

 small, the duration of the force is short, and the vertical 

 velocity remains constant during impact. In destroyers 

 the duration of the impact is from the first contact to 

 the full submergence of the bow; i.e., about a quarter 

 of the wave-encounter cycle. The vertical velocity is 

 variable from maximum at the beginning to zero at the 

 end. Attention should be paid to choosing realistic 

 velocities. The results of this investigation subsequently 

 can be used to evaluate the total impact force by the 

 strip method. 



Nomenclature 



Symbols listed at the end of Chapter 2 and in Appendix 



C apply unless otherwise stated. Additional symbols 



are as follows: 



b = damping coefficient 

 bj = damping coefficient caused l).v water 

 E = modulus of elasticity 

 G = shear modulus 



/ = moment of inertia of a hull section 

 k'AG = effective shear rigidity of a hull section 

 m = a mass; mass per unit of a beam's length 

 M = mass per unit length of ship structure, equipment and 

 load (tlie overl)ar may be omitted when there is no 

 ambiguity) 

 m" = hydrodynamic mass 

 n = number of nodal points; also used as a subscript for a 



vibration mode designation 

 P = impacting force 

 P{t) = impacting force as a function of time 

 P(j, /) = exciting force as a function of position and time 



p(l) = exciting force per unit of mass, also per unit of a beam's 

 length 

 q = damping factor (defined in Section 5.53) 

 r = radius of gyration of a hull section 

 an = characteristic numbers defined under equation (11) 

 6 = logaritlimic decrement 



^' Lewis and Gerard (1958) project 4-3-1 is here relevant. An 

 extension of this project to investigate the effect of rigidity of a 

 built-up structure was suggested by Lewis and Gerard in the 

 project III-3-1. 



