:c / 



t ~ 3 „ 



\ 



Several programs for the dynamics of ill or pan of 

 free-floating and moored systems have been written 

 at GE. Emphasis has been placed on modeling the 

 dynamics of surface buoys in heave, surpe, and pitch, 

 and in modeling subsurface moorings or suspended 

 systems. When necessary, surface and subsurface 

 models can be coupled to gain a totaJ picture of the 

 response of a system to the ocean environment. The 

 programs consider inertia forces, added mass, form 

 and friction dr.-ig, and variations in cable material. 



These programs have been developed for the dynamic 

 analysis of single-point moored ships or other surface 

 structures. Both programs assume the ship to be free 

 of motion restraint other than against sicady drift. With 

 this assumption, the dynamic problem reduces to one 

 of determining the effects of waves and current on the 

 surface object and then applying these effects id '.he 

 mooring cable along with steady drajr to determ.ine 

 tensions and deflections as a function of time. The 

 pscudodynamic solution is used for quick approvimaie 

 answers while more complete solution is gained from 

 the method-of-characieristics technique. According to 

 the authors of Reference 62, computer time required per 

 case is 15 minutes for the simplified program and 2 to 3 



puter is used. Nu listing is given in the refcrcmt:. 



This program dciermincs the dynamic behavior of 

 multileg mooring systems for sliiph or other surface 

 vessels in deep water. The assumptions are made that 

 the moored ship's motions arc essentially the same as 

 that of an unrestrained ship and that ship pitch and 

 heave moiion can be related to cable tensions by 

 catenary equations. For solution, the ship is given an 

 initial displacement from the calm water position to 

 balance drift caused by second-order wave forces and 

 then is assumed to oscillate about this position. Cable 

 tensions arc the sum of those due to drift and oscillarion. 

 A program listing is given in Reference 64. 



These programs arc both written in FORTRAN language 

 and have been developed: (1) to estimate the line tension 

 response of a surface buoy and taut cable to vravcs and 

 (2) to estimate the oscillatory motions of a submerged 

 buoy moored in an ocean currciii. The first solution uses 

 the mechanical impedance approach to obtain a transfer 

 function for the taut mooring system. The second solu- 

 tion uses the pendulum analogy and catenary equations 





Programs are operational 

 and proprietary. 



Programs arc operational 

 and proprietary. 



Program is operational. 

 Programs are operational. 



3 L 



Cables are elastic. 



Cables are extensible and 

 have most -real" cable 

 properties. 



Cables ore clasfic. 



(J) For the mechanical 

 impedance solution, the 

 cable is a scries of rigid 

 elements interconnected 

 by springs; (2) for the 

 pendulum analogy solution, 

 tJic cable must be of con- 

 stant mass per unit length 

 and mav be extensible. 



1 1 



Unknown, 



Hydrodymunic 

 damping. 



Nonlinear viscous 

 damping. 



Fluid-dynamic damping 

 is a linear function of 



,| 



Wind, wave, and current 

 forces. 



Steady wind and current 

 forces plus wave forces 

 as described by linear 

 theory. 



First- and second-order 

 surface-wave forces and 

 moments caused by 



Surface-wave and 

 subsurface current 

 forces. 



jj 



.Modified 

 Newmark and 

 Runge-Kutta 



integration of 

 equations of 



Two solution 

 types: (1) finite 

 difference/ 

 method of 

 cha-nctcristics, 

 <2) pscudo- 

 dyn.-imic 

 solution 

 neglecting 



inertia of cables. 



Mooring forces 

 due to drift 

 displacement 



vessel motion 



Two solution 

 types! {!> 

 mechanical 

 impedance/ 

 transfer fune- 

 tion;(2) pendu- 

 lum analogy/ 

 catenary equa- 



P 



Free- floating, 

 slack or taut, 

 single-point 

 mooring 



Single-point, 

 moored, surface 

 surface vessel. 



Multileg. 

 moored, 



vessel with 



surface buoys 

 in each leg. 



Taut single- 

 point mooring. 



1 i - 

 III 



" ~ " " ■ 



i li 



Ocea) Platform Syilcmn 

 r.cnrril Electric Company 

 Rc-tntry anil Environmental System 



Ph ladrlphia, PA 

 Comm (2151 82J-S362 



8. W. Wilson 

 Paudcna. CA 

 Comm(21.1)79)-57IO 



D. H. Gorbaccio 



Hycon Manufaccuring Company 

 .Monrovia. CA 



E. E. Ztmick 



} M. J. Cisarclla* 

 Carbolic University of America 

 Washingion. D.C. 

 •Commc202)6J5-5177 



C U Liu- 



J. A. Drclichan 



Civil Engineenng Laboratory 



Port Huencme. C\ 



'Comm(8lJ5>982-46U 



Autovon 3(.0.«13 



