Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Nonlinear Motions and Whipping Loads of High-Speed Crafts in Head Sea
Nonlinear Motions and Whipping Loads of High-Speed Crafts in Head Sea
Pages 157-170
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From page 157... ...
Several years ago, Chin, one of the authors, and Fujino5~8 developed a practical method, which is in principal based on the conventional Ordinary Strip Method synthesis but modified to be able to evaluate nonlinear hydrodynamic impact forces as well as dynamic lift in waves, for calculating vertical motions and wave loads of a high-speed craft which travels in regular head sea, and its validity was verified by comparing the computed motion and wave loads ls7 with experimental results performed by using a ship model of hard chine type as well as a ship model of round bilge type. Recently, it was confirmed further that this method also can be applied even to estimated vertical motions of fishing vessels in head sea With accuracy enough for practical user.
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From page 158... ...
The counter clockwise rotation around the y-axis and downward heave displacement are regarded as positive. The incident wave (w is described as (W=(acos (AX COST+ sinr+wet)
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From page 159... ...
are as follows fma: sectional hydrodynamic inertia force fmj: hydrodynamic force due to longitudinal variation of sectional heave added mass associated with vertical oscillatory velocity * fmj hydrodynamic force due to longitudinal variation of sectional heave added mass associated with vertital steady velocity component of constant forward speed.
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From page 160... ...
2.3.1 Nodal Superposition Method Form_lation Por modal superposition analysis, the mode shape functions wj are obtained by lyklestad'St3 method for a free-free Euler beam, the first 4 mode shape functions corresponding to vibration deformation, j=3-S are illustrated in Figure 3. Equations of motion derived from Equation (13)
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From page 161... ...
The nonlinearities of hydrodynamic forces related to the time-varying sectional hydrodynamic coefficients and hydrodynamic impact forces are treated in such a manner as described subsequently. The sectional hydrodynamic coefficients at several different prescribed drafts of a section are computed by Frank close-fit methods for each transverse section.
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From page 162... ...
(a2Iodal superposition calculation (called "10 The structure response is represented by modal superposition method in which the ship hull girder is assumed to be an Euler beam and mode shape functions used are obtained from lyklestad's method. The number n of mode shape functions taken in calculation is 6 in general, (that is, two rigid-body-motions and 4 vibrati
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From page 163... ...
In order to manifest the validity of the present nonlinear prediction of responses , the time histories of bending moments at square station 1 to 8 as well as C.G. acceleration and bow acceleration obtained by "F.E.~." calculation are shown together with the measured ones 0.06 .
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From page 164... ...
Fig. 14 Longitudinal distribution of vertical bending moment (Fn=0.70,1/L=~.7)
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From page 165... ...
The plausible reason of the discrepancy in time histories at hogging condition, in which the bow sections emerge from the water surface, between the predicted and the measured bending moments is that the incoming wave surface is assumed to be undisturbed even when the ship travels in waves at a high speed, namely, the effects of spay while planning occurred are not taken into consideration.
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From page 166... ...
21 (a) Time histories of bending moment by experiment and calculation (Fn=~.O,)
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From page 167... ...
It can be seen in this figure that although decreasing the shear rigidity may reduce sagging moment of midship remarkably, the hogging moment of midship may be increased, and the sagging as well as hogging moments acting at sections of fore-bodies may be increased significantly. However, it can be said that for the prediction of wave loads acting on the actual high-speed craft, neglecting shear deformation may underestimate the hogging moment, but has no significant effects on sagging moment.
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From page 168... ...
M " calculation method, which is principally based on a modif fed nonlinear strip method, and following the Timoshenko beam elment formulation, can be applied to estimate nonlinear motions and wave loads including whipping effects of a high-speed craft in head sea with accuracy enough for the practical point of view.
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From page 169... ...
Through the comparison between numerical prediction and elastic backbone model testing results,the present "F.E.II. " calculation method, which is principally based on a modif fed nonlinear strip method, and f allowing the Timoshenko beam elment formulation, can be applied to estimate nonlinear motions and wave loads including whipping effects of a high-speed craft in head sea With accuracy enough for the practical point of view.
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From page 170... ...
(22) APPENDIX B The elemental coefficient matrices [!
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