By Jean Bougis (auth.), Edwin Kreuzer (eds.)

Proceedings of the IUTAM Symposium on Fluid- constitution interplay in Ocean Engineering, held in Hamburg, July 23-26, 2007.

The research of gravity pushed water waves interacting with fastened or freely floating gadgets is an energetic and demanding box of analysis in ocean engineering. The actual prediction of enormous amplitude send motions or of marine constructions in serious seas continues to be a fragile challenge within the box of fluid-structure interplay. whereas 3-dimensional panel equipment have reached the nation of adulthood in linear sea-keeping research, the unique challenge, ruled by way of strongly nonlinear boundary stipulations, is much from being solved successfully. The imperative nonlinearities are linked to the variable wetted floor of the send hull or the floating physique and with the nonlinear hydrodynamic stipulations at the unfastened floor. additionally, marine constructions frequently needs to be modelled as multibody platforms instead of a unmarried physique. This factors extra difficulties as a result of wave slamming on floating and stuck buildings. moreover, difficulties resembling coupled structural habit of submerged or floating platforms in addition to a number of wind results need to be thought of for the correct layout of offshore structures.

This e-book collects contributions from prime scientists engaged on the subsequent themes: Ocean waves, probabilistic versions of sea waves, fluid-loading on buildings together with pipes, cables, drill-strings etc., habit of floating platforms, balance and capsizing of ships, coupled structural habit, sloshing in tanks, CFD validation and verification.

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7 Conclusions We have seen, the consequences of non-linearities and coupling effects on floating breakwaters eigenvalues and take a prominent part in the design of floating 12 Jean Bougis breakwaters anchored on piles. For some exposed sites, the greatest problem is no longer set in terms of extreme loads but in terms of stiffness and of natural periods. 5 s. RA0 plotted on Fig. 1 shows that this usual approach is inadequate as early as anchorage stiffness is nonlinear. If equivalent linear damping verify α2 > α2 (1 − α2 )2 > |μ|, or better 4α4 > 4α4 (1 − 2α2 ) > |μ|, RAO is broken in two parts and low frequency amplification concerns only periods greater than 5 or 10 times eigenperiods.

If equivalent linear damping verify α2 > α2 (1 − α2 )2 > |μ|, or better 4α4 > 4α4 (1 − 2α2 ) > |μ|, RAO is broken in two parts and low frequency amplification concerns only periods greater than 5 or 10 times eigenperiods. We must try to obtain a good enough linearity of anchorage stiffness, in order to eliminate the three risks of eigenperiod sliding, superharmonic resonances and combined resonances. This objective can induce us to increase the flexural rigidity of the pile. If the depth of water or the thickness of soft soil is too important, it can be more convenient to fill up piles with concrete than to increase wrongly the steel thickness.

In order to evaluate the unsteady contribution to the pressure, the harmonic properties of φ˙ are exploited. In this way we arrive to a second boundary integral equation in terms of ϕ. ˙ As for the velocity potential, a Dirichlet condition is assigned on the free surface, where ϕ˙ = −|∇ϕ|2 /2, and a Neumann Hydrodynamic Loads during Water Entry of a Flat Plate 23 boundary condition is assigned on the body surface. It can be shown that, for a flat and horizontal body surface, and for a constant entry velocity, it is [9] 1 ∂uτ ∂ ϕ˙ = −wn − wn uτ , ∂n ∂τ r where τ is the parameter along the body surface, uτ is the tangential velocity component of the fluid and wn is the normal velocity component of the body.

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