Devn 



(ii) Furthermore, if the period of the wave is in the 

 range between the period of the natural rolling motion 

 and half that of the natural pitching motion and if the 

 static stability in pitching is small, then the motion 

 of the buoy consists of three parts : heaving, rolling 

 and pitching ; two combinations exist, one with a mo- 

 derate heave value, the other with a larger heave va- 

 lue ; in each case the amplitude of the pitching mo- 

 tion varies irregularly from one oscillation to the 

 next one and gives the impression of being a random 

 function of time. 



The above phenomena cannot be predicted from a li- 

 nearized theory. The phenomenon described in (i) 

 can be explained by the non linearity of the restoring 

 force in pure heave motion ; that described in (ii) by 

 the existence of a term in 6 Z (8 = pitch angle, Z 

 = heave) in the equations of rolling and pitching. 



In the case of irregular waves it is proposed for the 

 rolling and pitching motions a stability criterion simi- 

 lar to that of J. B.Keller and G.F. Carrier for tsuna- 

 mis. 



INTRODUCTION 



For some years now, theoretical studies have been devoted 

 to the motion of spar buoys in regular waves. In these works the 

 equations of the heaving motion Z , surging motion X and pitching 

 motion 8 are generally linear ( [l] , |_2j , [3] ). In reference [4] 

 experiments performed on circular cylindrical buoys, of slenderness 

 (draft / radius) larger than 5, in regular and irregular waves are 

 reported. It appears from the results presented in [4] that 

 J. N. Newman's theory is well verified under the condition that an expe- 

 rimentally determined added mass be included in the heaving equation. 



In the present paper we present the results of experiments on 

 spar buoy models in regular and irregular waves. In contradiction 

 with reference [4 J , motions not predicted by Newman's theory were 

 observed. These particular motions cannot be explained but by the pre- 

 sence of non linear terms in the equations, which come from the fact 

 that in the vicinity of its natural heaving frequency a spar buoy is sub- 

 mitted to vertical oscillations of large amplitude, the damping force 

 being very weak. It is not possible, then, to neglect, even as a 

 first approximation, the variation of the instantaneous waterline area 



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