11.6 Numerical Examples
441
Station
Ship’s weight
(kN)
Virtual weight
of water
(kN)
Moment of
inertia
(m 4 )
Effective shear area
(m 2 )
1
520
0
3.5
0.080
2
2880
250
9.6
0.194
3
2900
1030
14.3
0.238
4
2260
2450
15.6
0.238
5
2070
4910
18.6
0.254
6
3760
7420
21.4
0.258
7
4830
9660
24.2
0.252
8
5160
1,1120
29.5
0.250
9
5880
1,1740
29.5
0.280
10
5780
1,1860
29.5
0.275
11
6540
1,1640
29.5
0.298
12
4310
1,0890
32.5
0.241
13
2870
9300
28.0
0.241
14
2870
7230
25.1
0.256
15
2980
4710
23.2
0.250
16
2730
2340
20.3
0.263
17
2320
1060
17.5
0.260
18
2540
280
16.1
0.290
19
2190
60
12.9
0.226
20
770
0
5.1
0.123
References
1. O.C. Zienkiewicz and R.L Taylor, The Finite Element Method, Fourth Edition, McGraw Hill,
1989.
2. M. Mukhopadhyay and S. Guha, A method for determining natural frequencies for vertical
vibration of ships, Marine Engineering Division, Journal of the Institution of Engineers (India),
May 1980, pp.36-39.
3. G. Anderson and K. Norrand, A method for the calculation of vertical vibration with several
nodes and some other aspects of ship vibration, Transaction of the Royal Institution of Naval
Architects, V. 111, 1969, pp. 367-383.
4. D.K. Sunil and M. Mukhopadhyay, Finite element free vibration analysis of ship girder, Journal
of Institution of Naval Architects, India, December 1993, pp. 83-92.
5. M. Mukhopadhyay, Free vibration of free-free beam with rotary inertia effect - a flexibility
matrix approach, Journal of Sound and Vibration, V.125, No.3, 1988, pp.565-569.
6. F. H. Todd, Ship Hull Vibration, Edward Arnold Publishers Ltd., 1959.