Analyses of Multiple-Float-Supported Platforms in Waves 



The present study also applies the close -fit source distribu- 

 tion method pioneered by Frank [2 8J . We assume two arbitrarily 

 shaped bodies, which do not have to be either symmetrical about their 

 vertical midplanes or to be symmetrically disposed with respect to 

 each other. Furthermore, the two bodies may be unconnected or con- 

 nected either rigidly or elastically. 



This investigation, based on two-dimensional linearized theory, 

 considers both the radiation and diffraction problems for two arbi- 

 trarily shaped cylindrical bodies floating in a train of beam waves ; 

 the hydrodynamic inertial and damping forces and moments due to 

 swaying, heaving and rolling of the cylinders on a calm water surface 

 and the forces and moments induced by beam waves on the fixed cyl- 

 inders are evaluated. 



Brief descriptions will be given of the methods used to evaluate 

 the unknown velocity potentials for the radiation and diffraction pro- 

 blems. Since the fundamental velocity potential of a two-dimensional 

 pulsating source of unit intensity located below the free surface and 

 satisfying the required hydrodynamic conditions inside and on the 

 boundaries of the entire deep-water domain is a well-known solution 

 stated by Wehausen and Laitone [29J , it is only necessary to discuss 

 here the kinematical boundary conditions on the body contours. 



Two applications of the theory will be considered in detail : 

 1) the analysis of the hydrodynamic forces on two rigidly connected 

 cylinders and, 2) the relative heaving motions of two unconnected 

 bodies in close proximity. Results of calculations for these cases will 

 be presented and discussed. The case of a pair of three-dimensional, 

 vertical body-of -revolution floats, in close proximity will be discuss- 

 ed on the basis of experimental results. 



KINEMATIC BOUNDARY CONDITIONS 



The Radiation Problem 



Consider two arbitrarily shaped parallel cylinders oscillating 



in prescribed (arbitrary) modes of motion, with given amplitudes and 



phases, on or below the calm water surface in the form 



(m ) 



[S] = S a e" 1 ^ 

 u a a 



(m ) -i(e +U) 



[Si = S K b e SaSb (11) 



b b 



807 



