SOME TOPICS IN INDUSTRIAL AND APPLIED MATHEMATICS by edited by Rolf Jeltsch, Ta-Tsien Li, & Ian H Sloan

By edited by Rolf Jeltsch, Ta-Tsien Li, & Ian H Sloan

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FREQ. 01) MODE 7 FREQ. 8 (0·96) - --:. :. -,. - MODE 1 FREQ ---=~~- --- 66·5 (-) MODE 6 FRED. GQNAl MODAL ADDEO MASS IO'J20----------L----100 XX) «xJ (b) EXTREME AFT END VERTICAL ~-- - - - ... -----------FREUUHICY (c/m,nl-·- . - - - - - - . 60 c/mln (b) Mobilities to Propeller Arch; Products Tanker FIGURE 3. Example Response Calculation; Natural Modes and Response Amplitudes 57 to be coupled. Results using the techniques outlined above have also been compared with approaches of other organisations, see Ref.

4. MODELLING THE FLUID FORCES The reaction of a fluid which is in contact with a vibrating structure has two components. These are respectively in-phase and out-of phase with the acceleration. In the usual mathematical approach to the problem it is assumed that the fluid is incompressible and inviscid and the motion is irrotational. In this case, that part of the fluid reaction which is in-phase with the acceleration may be treated as an added mass. The out-of phase component represents free surface damping effects at the lower frequencies or represents compressibility at the acoustic range.

With the advent of computers, finite element methods gained popularity based on early work in the aerospace industry. Today, alternative calculation procedures for ship vibration are fairly well documented and their applicability has been compared, based on detailed full-scale measurements, using natural and/or artifical excitation. Surface singularity methods have been employed to calculate the influence of the surrounding water and the fluid contained in internal compartments. The influence of the fluid is exhibited as an added mass and, to a lesser extent and depending on a non-dimensional frequency parameter, an added damping.

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