Pien and Lee 



/ds / p n. d^= P / ds / 



(j w n + <|). d ) 0. d-£ 



o i x i ^n ~i 



/I " C(S) 

 (J).* d£ + £ (a, 2 A. u (x) + jco B.. (x)) 

 1 T In |^2 lk J lk v " 



6 C ^ 



+ u £ 2 «ko<J" a ik (x > - b ik< x » < 30 > 



where a jk (x) and b ik (x) are the sectional added mass and dam- 

 ping of the cross section at x. The expressions of A jk (x) and 

 B jk (x) in terms of sectional added inertia and damping are almost 

 identical to those for A jR and B ik shown in Table 1, except 

 that the integrals in the table should be replaced by \g A , and A jk 

 and B.. should be replaced by A., (x) and B.. (x) . For instan- 



IK IK IK 



ce, 



A 35 W " ) X sa 33 (s)dS -^ B 33 W 



where 



I 

 (' 



it 



B 33 (X> = /, b „< s > ds 



Returning to Equation (24), we can now write 

 X 



-" 2 /» m 



f 

 It 



- "U ^f (J "o n 2 + <t> 2 -&>*I dl 



- W 1 j * 2 * ln ** ' < « 2 A 22 M + i . B 22 (x)) i 2Q 



c(x) 



- ( c/a 24 (x) + j M B 24 (x) ){ 2Q - ( " 2 A 26 (x) + j u, B 26 (x))^ 



6 

 + U £z t ko ( J"*2k< x > - b 2k< X >> < 3 » 



in which 



482 



