Motion and Resistance of a Low-Wat erp lane Catamaran 



the change of pressure distribution due to the oscillatory motion of 

 the ship. We assume that the motion displacements £j(t), i = 1, 2, 

 .... 6 are already known, and for brevity we will dispense hereafter 

 with the term e " w with the understanding that the time dependence 

 of the loading quantities to be studied is harmonic. 



The types of loading to be considered can be divided into 

 three major parts; these are : 



Shear Forces (figure la) 



a. Transverse shear in the 'Oyz plane 



b. Vertical shear in the Oyz plane 



c. Transverse shear in the Oxy plane 



d. Vertical shear in the Oxz plane 



Bending Moments (figure lb) 



a. Transverse bending (M ) 



b. Horizontal bending (M ) 



c. Longitudinal bending (M ) 



Torsion Moments (figure lc) 



a. Yaw torsion moment (T ) 



b. Pitch torsion moment (T ) 



In the sequel the symbols in the parentheses shown previously will 

 be used to denote the specific types of loading. 



If we let fp and f 3 denote, respectively, the sectional 

 heave and sway forces due to the mass inertia, and R 2 and R3 

 denote the horizontal and vertical restoring forces, then the shear 

 forces at section x can be expressed by 



V (x) = Ij (s) ds - / ds f p n. di - R. (24) 



A l h< c(s) 



for i = 2, 3 1 1 



-f 2 (s) = -c 2 m(s)( ^ 2Q+ s ^ -z(s) f ) (25) 



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