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                    TABLE 3
      COMPARISON OF EIGEN ANGULAR FREQUENCY
      OF VLFS BY ANALYTICAL METHOD AND FEM


                                                 3.




                                                  0.   0.25   0.5   a75   LO
                                                              WkW~
                                            Figure 3:   Frequency  response  amplitude
                                                     of  horizontal  deflection  at  the
                                                     free end of main structure under
                                                     low mooring rigidity

     b=6.963 X 104N/m2,for case Low and
     L=3.920X 104N/m2 for case High





                                                   .   2.



                                                       0.   0.25   0.5
                                                                   Angul:&.(d$
                                             Figure 4:   Frequency  response  amplitude  of
      Figure 2:   Frequency response amplitude of     deflection at the top end of dolphin
              deflection at the top end of dolphin    located  at  the  free  end  of  the
              located  at  the  free  end  of  the    structure  under  low  mooring
              structure under low mooring rigidity    rigidity
      The algorithm used consisted of a modified Newmark's  family of equations with automatic time step
      feature and Newton-Raphson's  Method.
      4.3 Calculating Case and Results

      4.3. I  Mooring clearance
      As a study case, we calculated the time history of combined model under the regular wave force. The
      regular force is assumed as following.
               F, = F, sin( k-x, - o I)                                    (8)
      where  F  is wave force,   (=2z   )is circular frequency of wave force, x , is the coordinates of the
      node,   (=k/cos(a))is the degree of incident wave.
      In numerical computation, we obtained the time history of the axial forces of each mooring fender and
      the deflection of the calculating points on the structure.  We show only some selected figures due to
      page limited.
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