Unstable Motion of Free Spar Buoys in Waves 



S (z) Section area of buoy 



S (f) Spectral density of relative motion 

 ss 



Sop (f) Spectral density of waves 



T Period of pitching motion 

 P 



T Period of rolling motion 

 r 



T Period of relative motion 

 s 



T Period of irregular waves 

 v 



T Period of regular waves 

 w 



"\y" Instantaneous immersed volume of buoy 



W Displaced volume of buoy in calm water 



X Surge displacement of buoy 



Y Sway displacement of buoy 



Z Heave displacement of buoy 



a = z ' - z' 

 C G 



a Acceleration of fluid particles due to orbital motion of 

 o . 



the on-coming waves 



a 

 ox 



= (a . ~x5 



a = (a . z ) z 



ozo o o o 



f Frequency 



f Natural frequency of heaving motion 



f Natural frequency of pitching motion 

 



g Acceleration of gravity 



i = V 



Characteristics of the upper part of buoy 



k Wave number , 2tt 



A 

 m Buoy mass 



m Added mass of buoy in the x direction 



xx 



m Added mass of buoy in the y direction 



yy 



m Added mass of buoy in the z direction 



1077 



