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By C Guedes Soares; Joško Parunov

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Extra resources for Advanced ship design for pollution prevention : proceedings of the International Workshop "Advanced Ship Design for Pollution Prevention", Split, Croatia, 23-24 November 2009

Example text

Another approach could be to use just the frequency domain RAO values. This will not be correct if it is based on the linear motion calculated in the frequency domain. Therefore a Fourier transform of the seakeeping velocity is used to obtain the amplitude and phases at different frequencies. These results in a total radiation force which is very close to the radiation force calculated by the seakeeping program. The frequency content of the velocity in the earth reference frame is equal to: • The retardation function and convolution integral has to be evaluated for every point at the structural mesh.

RAO of the stress at a particular finite element for different wave headings. g.  RAO of the vertical bending moment at midship section for different wave headings. 1 Non linear seakeeping model (19) ω z ) ( i) Nfreq k ∑ ρ gζ i t, xw ,ω e i=1  z p fk = ρ gζ t, xw  1 −  ζ t, xw  ( p fk = ( ) ( )     ( ) ( ) z < 0 and z < ζ t, xw z ≥ 0 and z < ζ t, xw ( z ≥ ζ t, xw p fk = 0 ) (23) The hydrostatic pressure is equal to: z < 0 and z < ζ (t, xw ) z ≥ 0 or z ≥ ζ (t, xw )  ph = − ρgz   ph = 0 where: m Genuine mass matrix A Added mass matrix B Damping matrix K Retardation (memory) functions (24) The diffraction force is linear and equal to: → → f D Diffraction force fk (20) ζ i (t, xw , ω ) = ζ a (ω i ) cos ω it + εζ (ω i ) + xw k (ω i ) (21) Linear seakeeping analysis can be used with fair accuracy as long as the wave height remains small.

The angle of cross-section rotation is caused by the bending deflection ϕ= ∂ wb . ∂x Bw = EI w ∂ x2 , (4) 3 ∂ ws ∂ wb Q = GAs = − EI b . ∂x ∂x 3 ∂2 ψ t . ∂ x2 f e = k eδ e + meδe , (5) (12) (13) where fe is nodal forces vector, δe is nodal displacements vector, ke is stiffness matrix, and me is mass matrix. , Figure 2. ψ = ψ t + ψ s . (11) 1D FEM procedure for vertical ship hull vibrations is well known in literature. Coupled horizontal and torsional vibrations are a more complex problem. Due to analogy between bending and torsion the same shape functions, represented by Hermitian polynomials, are used.

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