Analyses of Multiple-Float-Supported Platforms in Waves 



up (a minimum number are required to afford stability against cap- 

 sizing). The resiliency of the structural components, including the 

 floats themselves, which may be inflatable reinforced fabrics, pose 

 certain interesting hydroelastic questions. Several hydroelastic aspects 

 have been and are being studied but these will not be treated in this 

 paper. 



ANALYSIS OF VERTICAL FLOAT HEAVE MOTION 



Elementary Equation of Motion 



In the configuration depicted in Figure 26, the net buoyancy 

 comes from the portion of the float above the hinge, which is located 

 some distance below the Stillwater level. The float shape, which is 

 enlarged below the waterline, is intended to minimize the wave -induc- 

 ed vertical forces transmitted to the deck and structure, and thus 

 minimize deck motions over a "sufficient" range of wave frequencies. 

 The hinge is introduced to alleviate lateral loads in the float and in the 

 structure : the wave-induced forces produce pendular motions of the 

 lower part of the float (which is called an "attenuator") which relieve 

 the elastic stresses and transmitted loads which would develop without 

 the hinge . 



Since the deck structure is assumed to be quite flexible, the 

 (linearized) equation for the heave (z) motion, neglecting elastic re- 

 storing forces, can be expressed simply as 



where 



pVz = - m" z - Z.z - Z z + Z.f (30) 



z z s 



V = total displaced volume of float and attenuator 



m" = added mass 



Z. = damping force rate 



Z = buoyant re storing-force rate = pgA 



A = water plane area 



w 



Z = wave-induced vertical force per unit wave 

 elevation 



f = wave elevation 



If the deck's elastic restoring-force is to be taken into account, 

 a term such as EI-§^z_ must be incorporated to describe motion in 



821 



