Wave Induced Foraes and Motions of Tubular Structures 



Thus, it is seen that the use of such equivalent linearization 

 requires a prior knowledge of the amplitude of the motion. No 

 difficulty is introduced by this in the case of the wave force on a 

 stationary member. However, the amplitude is unknown for the 

 absolute motion of the member. This leads to the necessity for an 

 iterative solution in which we first assume an amplitude of motion, 

 compute the equivalent linear coefficient, and then solve the equa- 

 tions of motion using this value. This solution then Is used to com- 

 pute a refined value of the linear drag coefficient, which Is used for 

 the second solution of the equations of motion, and so on. It Is 

 questionable whether the approximations Involved warrant more than 

 two Iterations, as noted by Burke [ 1969] . 



Hydrostatic Forces 



A floating body which Is displaced In heave, pitch, or roll 

 from Its equilibrium position experiences hydrostatic forces pro- 

 portional to these displacements as a result of the changes Induced 

 In the Immersed volume. There will be no forces In surge, sway, 

 or yaw since these displacements , which are parallel to the free 

 surface, cause no change In the Immersed volume. 



These forces. Including coupling terms, are computed by 

 standard naval architectural formulas. Thus, the vertical force 

 resulting from a small heave displacement, x , is given by 



Fy = - PgA^Xg, (18) 



where A^ Is the waterplane area. 



Similarly, the moments of this force about the x- and z- 

 axes (static coupling terms) are given by 



M = pgA^z Xg 



The roll and pitch moments resulting from small angular dis- 

 placements are given by 



M = - pgVGMa, (20) 



where GM Is the appropriate metacentric height, V Is the volume 

 displaced by the structure, and a Is the small roll or pitch angle, 

 either x^ or Xg In the notation of Eq, (6). 



Finally, the force In the y-dlrectlon resulting from a small 



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