THE SECOND-ORDER THEORY FOR NONSINUSOIDAL 

 OSCILLATIONS OF A CYLINDER IN A FREE SURFACE 



Choung Mook Lee 



Naval Ship Research and Develoipment Center 

 Washington^ B.C. 



ABSTRACT 



A nonlinear hydrodynamic response resulting from 

 vertical oscillation of a horizontal cylinder in a free 

 surface at the sum of two monochromatic frequencies 

 is investigated. The fluid surrounding the cylinder is 

 assumed incompressible, its motion irrotatlonal and 

 its depth infinite. 



It is shown for the case of a semi- submerged circular 

 cylinder that when the two frequencies are close to 

 each other the hydrodynamic force associated with the 

 difference of the two frequencies is greater than the 

 steady force. In the limit as the two frequencies 

 become equal the above two forces also become equal. 

 It therefore appears reasonable to include the differ- 

 ence-frequency force in the calculation of the maximum 

 steady force when the excitation of a body consists of 

 narrow-band frequencies. 



I. INTRODUCTION 



The hydrodynamic problem dealing with a horizontal cylinder 

 undergoing a vertical simple harmonic motion in a free surface has 

 been investigated by many authors. Ursell [ 1949] treated a semi- 

 circular cylinder using the method of multipole expansion and ob- 

 tained the pressure distribution, added inass , and damping of the 

 cylinder. Later Tasai [ 1959] and Porter [ i960] extended Ursell's 

 work to cylinders of ship-like sections using conformal mapping. 

 Frank [ 1967] dealt with the foregoing problem by the Green's func- 

 tion which resulted In a distribution of singularities. Lee [ 1968] , 

 following Porter's work, extended the potential solution to second- 



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