Unstable Motion of Free Spar Buoys in Waves 



SECTION II 



THEORETICAL INTERPRETATION OF THE 

 RESULTS OF EXPERIMENTS IN REGULAR 

 WAVES 



The experiments , the results of which we have presented in Section 

 I , show that the spar buoy is far from behaving as a linear dynamic 

 system . It is possible to interpret these results qualitatively and 

 sometimes quantitatively using a non linear theory . This theory is 

 simply set by slightly modifying J.N.Newman's equations . In these 

 equations some volume integrals were calculated supposing that the 

 buoy heave was infinitely small . We take back these integral calcu - 

 lations making allowance for the finiteness of the heave amplitude . 



I - GENERAL EOUATIONS OF MOTION - 



The following classical assumptions are made : 



- The buoy is a slender body (H/R » l) 

 '- Oncoming wave is Airy wave 



- The exciting forces are computed using Froude Krilov hypothesis 



With these assumptions , the equations of motion with 

 six degrees of freedom are obtained reasoning as in [_2j 



ff + oi-^H +[WJ[v] + [r] = [f] + [p] 



with 



[r}= 



f 



h 



d \r 



p ( G p A T) d ^ 



1031 



