\Jave Induced Forces and Motions of Tubular Structures 



on the platform's performance by the resulting wave motions. 

 Second, given a set of sea conditions and platform requirements, we 

 may investigate a family of platform configurations to determine 

 those members of the family which will be able to perform the 

 specified mission under the stated sea conditions. This kind of 

 analysis, in turn, might form a part of a more extensive system 

 study aimed at determining the most cost effective platform system. 

 As a third function, the force distributions on structural members 

 which are obtained during the force and motion analysis may be 

 used in connection with the detailed structural design of the platform. 



The general procedure followed in analyzing the dynamic 

 behavior of such a platform is to assume that it behaves as a rigid 

 body having six degrees of freedom. The external forces which 

 excite the motion of the structure are associated with the fluid motion 

 relative to the structure, and with the structure's mooring or position- 

 ing system. Two alternative methods are available for the computa- 

 tion of the fluid forces. In the first, the fluid is assumed inviscid 

 and its motion irrotational , and we proceed on the basis of classical 

 hydrodynamic theory to seek a solution to Laplace's equation in the 

 fluid region subject to certain boundary conditions. These include 

 kinematic boundary conditions on the free water surface and on the 

 wetted surface of the structure itself, a constant pressure dynamic 

 boundary condition on the free surface, a dynamic boundary condition 

 on the wetted surface of the body, which is derived from the rigid 

 body equations of motion, and other conditions far from the body 

 which are necessary for uniqueness of the solution. This approach 

 yields great insight into the fundamental nature of the fluid phenomena, 

 and is exact within the limits of the necessary fluid idealization and 

 motion linearization. Its implementation, however, is beset with 

 almost insurmountable difficulties unless the geometry of the body is 

 extremely simple. 



The second method is less exact in principle, but provides 

 approximate means of including real fluid effects and of dealing with 

 geometrically complex, realistic configurations. This procedure, 

 which is employed in the present analysis, is termed "hydrodynamic 

 synthesis. " Here we consider the complex structure to be assembled 

 from a group of simpler bodies whose individual hydrodynamic pro- 

 perties are known, perhaps as a result of an analysis of the first type 

 above. A fundamental assumption is then made that the hydrodynamic 

 force on the assembled structure may be computed by taking the sum 

 of the forces of all of the component members. In the simplest case , 

 these forces are computed as though, each member were completely 

 remote and independent of the rest of the structure, but subject to the 

 same pattern of body and fluid motions. The forces connputed in this 

 way might be refined by introducing modifications to the fluid flow to 

 account for the hydrodynamic Interaction between adjacent members. 



The result of this hydrodynamic synthesis Is a system of 

 hydrodynamic forces acting upon the assembled structure, containing 

 terms dependent upon the Incident wave system and upon the motion 



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