Page 42 - Rekayasa Pantai

O T L 1 (3.14)
E k =    (u 2 + w 2 ) .dzdx .dt
− h O O 2
u =   = agk cosh k (h + ) z cos(kx − ) t 
(3.15)

-
x  w cosh kh
  agk sinh k (h + ) z (3.16)
w = − = sin(kx − ) t 
z  w sinh kh
Dari persamaan dispersi tanh kh = w 2 (3.17)
gk

coshk (h + ) z
Jadi u = aw cos(kx − wt ) (3.18)
sinh kh

sinhk (h + ) z
w = aw sin(kx − wt ) (3.19)
sinhkh

Maka

1 (  aw) 2 O T L
).
E =  cosh 2 k (h + ) z cos 2 (kx − wt ) sinh+ 2 k( h + z sin 2 ( kx − wt)  dxdz. . dt
k
2 sinh 2 kh − hO O
O z  sinh k 2 (h + ) z  O
 cosh 2 k( h + z) dz =  + 
− h  2 4 h −  h

h sinh . 2 . kh
= +
2 k 4

h  kh sinh2 + 2 . kh 
=  
2  2 kh 

O h  − kh sinh2 + 2 . kh 
 sinh 2 k( h + z) dz =  
−h  z 2 kh 

L T
 cos 2 (kx − t )dx. dt = 1  ( 1+ cos ( 2 kx − t ) dtdx.
2
O O

1 T L
=  x + sin ( 2 kx − t)  dt
2 O O

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