engleski

Second order internal loads on floating bodies

This note is devoted to the evaluation of the second order internal loads on the floating bodies oscillating about their mean position under the action of an monochromatic incident wave field. The internal loads are defined, in the usual manner, as a difference between the hydrodynamic forces and inertial forces at a given section. As far as the hydrodynamics is concerned, the calculations are usually performed for a linear case. Due to the assumptions of the linear theory (hydrodynamic model limited by the mean water level z = 0 and mean wetted surface of the body, simplified free surface condition, ...) some unnatural results occur, notably the fact that there is no difference between the sagging and hogging moments. This lack of the linear theory can be supressed only by introducing the different kinds of nonlinearities in the model. In principle, any kind of nonlinear aspects will produce the difference between the sagging and hogging moments, so that some authors introduce just the hydrostatic nonlinearities associated with the integration of the hydrostatic pressure under the exact linear wetted surface of the body (the most easy term to calculate). This, of course, is not correct way to treat the problem because the nonlinearities introduced by other effects (nonlinearities of the free surface, dynamic pressure under the wave profile, quadratic term in Bernoulli equation, ...) can influence the results and sometimes even cancel the effects of the hydrostatic nonlinearities. Thus, the coherent way to treat the problem, should be the evaluation of all nonlinear effects at the following order of approximation, linear theory being considered as a first order one. This leads us to the formulation of the second order hydrodynamic problem which has already been used successfully in the studies of global behaviour (slow drift oscillations, springing excitation, ...) of some offshore structures (semi- submersibles, TLP, ...). The present work was started with the idea that only when we are able to evaluate the importance of different effects we can be (hopefully) in position to eliminate some of them. Otherwise it will be dificult to conclude something serious.

2nd order internal loads; monochromatic incident wave; nonlinear effects

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