Page 305 - Introduction to Naval Architecture

290 VIBRATION, NOISE AND SHOCK

Tabte 11.2

L/B 5 6 7 8 9 10 11 12 13 14 15

,700 .752 .787 .818 .840 .858 .872 .887 .900 .910 .919
/ 2
J 3 .621 .675 .720 .758 .787 .811 .830 .845 .860 .872 .883

Note Ji and J s are for two- and three-node vibrations respectively.

kinetic energies of water in three-dimensions relative to two-
dimensions.
Values of/for two- and three-node vibration (/ 2 and/ 3 respectively)
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of ellipsoids of varying length to beam ratio were calculated to be as in
Table 11.2. These/values are applied to the total virtual added mass
calculated on the basis of two-dimensional flow. They are necessarily an
approximation and other researchers have proposed different values,
10
Taylor proposed lower/values as follows:
L/B 6.0 7.0 8.0 9.0 10.0
/ 2 .674 .724 .764 .797 .825
/s -564 .633 .682 .723 .760

Research using models has been done to find added mass values. One
11
such investigation found the Lewis results for two-dimensional flow
agreed well with experiment for two-node vibration but higher modes
agreed less well. It was found that for ship shapes:

These/values associated with the Lewis results for two-dimensional flow
should give a good estimate of virtual added mass for ship forms in
various vibration modes.

Rotary inertia
The simple formulae given above for a beam with a concentrated mass
assumed that the masses executed linear oscillations only. In the
relatively deep ship hull the rotation of the mass about a transverse axis