Wave Induced Forces and Motions of Tubular Structures 



The force system acting on the structure comprises hydrodynamic 

 forces resulting from wave and platform motion, hydrostatic forces 

 from the changes in displaced volume associated with static displace- 

 ments of the platform and the restraining forces exerted by the 

 positioning or anchoring system. 



ni. COMPUTATION OF THE FORCES 



The total hydrodynamic force exerted on the body is assumed 

 to be composed of three parts: 



(1) The force resultant of the pressure exerted by the un- 

 disturbed incident wave train on the stationary body in 

 its mean position. 



(2) The force resulting from the disturbance of the incident 

 waves by the body occupying its mean position. 



(3) The force resulting from the motion of the body computed 

 as though it undergoes the same motion in calm water. 



In a formalized linear analysis, these terms would be associ- 

 ated with velocity potentials representing the incident wave train, 

 a diffracted wave train, and the waves generated by the motion of 

 the body. The force represented by (i) above, i.e. , that part ob- 

 tained by neglecting the effect of diffracted waves and body motions , 

 is termed the Froude-Krylov force. 



Procedures based on assumptions similar to these have, as 

 previously noted, proven successful in predicting the motions of ships 

 in waves. The present situation is somewhat simpler than the ship 

 case because the structure has no forward speed. 



As noted in the Introduction, we shall obtain the total force 

 on the structure by computing the force separately on each member 

 of which the structure is conaposed. Two principal assumptions will 

 be made in computing these forces. First, each member is assumed 

 to be either a cylinder whose cross sectional dinnensions are small 

 compared to the lengths of both the cylinder and the incident waves, 

 or the member is a small pontoon (point volume) all of whose di- 

 mensions are small compared to the incident wave lengths. Second, 

 all hydro dyncunic interaction effects between adjacent members will 

 be neglected, thus the force on an individual member will be com- 

 puted as though the member occupies its mean position in the field 

 with all other members absent. 



In Fig. 1 , we show a cylindrical member located In the flow 

 field corresponding to a train of waves and undergoing motions cor- 

 responding to the rigid-body motions of the entire structure. The 

 force per unit length at a given point along the length of the member 



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