Unstable Motion of Free Spar Buoys in Waves 



SECTION III 



ROLL BEHAVIOUR OF A SPAR BUOY IN 

 MONODIRECTIONAL IRREGULAR WAVES 



I - INTRODUCTION 



It seems that no paper has been published to-date on the 

 rolling motion of bodies in monodirectional irregular waves . At 

 least the author has been unable to locate any . One may quote 

 Kastner's study I 20J about the righting arm of a ship in a longitudi- 

 nal irregular sea . In a sense , his study is a continuation of 

 Kerwin's theory but it does not deal with the effect of the irregular 

 variations of the righting arm on the rolling motion of the ship . 



From a mathematical point of view , the problem of the 

 rolling motion of a spar buoy is similar to various other problems 

 of mechanics (for example : simply supported beam subjected to 

 stochastic axial load ; vibrating string when the distance between 

 its ends varies stochastically) . All these problems are related to 

 the study of non- autonomous stochastic dynamical systems . Many 

 results exist for these systems but the most interesting one seems 

 to be that of G. F. Carrier I 21 J . In the present Section , the rolling 

 motion of the spar buoy is studied by using Carrier's theorem whose 

 statement will be given in the next paragraph . The validity of rol - 

 ling criterion is verified experimentally . 



II - HYPOTHESES FOR CALCULUS - 



In this Section we use equations (II -5. 1) and (II -5. 3) 

 with the following simplifications : 



(2) 

 N pp 



h = CD 



1063 



