Lee 



where a and a. are real constants 

 2n+i 



Points on the surface of the cylinder at its mean position are 

 given by 



(4) 



S. , \ a2n+i COS (Zn + l)^? 



00 J 



K ! ^ V apn-M sin(2n + l)Qrf 

 y^=a Kosinor- > ^^^^^^^V -\ ' 



where X.q is the radius of the reference circle. When the cylinder 

 is at the rest position its hcdf breadth and draft are given respectively 

 by 



h = ^^{\,0), (5) 



d= \y^{\^,-iT/Z)\. (6) 



The forced motion of the body Is assumed to be the sum of 

 two vertical simple harmonic motions with different frequencies. 

 The motion of a point fixed In the body Is expressed by 



y(t) = hQ{sln cr,t + sin cr^t) (7) 



where o-| Is greater than a. and h^ represents the annplitude of 

 the Individual simple harmonic motions. 



The fluid Is assumed to be Incompressible and Its motion to 

 be irrotatlonal so the continuity of miass In terms of velocity potential, 

 $(x,y,t) Is expressed by 



{^'■l^)^-^"^-°- (8) 



The boundaries of the fluid are the free surface which extends 

 to Infinity along both the positive and negative x-axes, the fluid 

 bottom which is at Infinity, and the Immiersed surface of the cylinder. 



If we let the equation of the free surface be expressed by 



y = Y(x,t), |x| > b, (9) 



908 



