Hydrostatic equilibriumΒΆ

We simulate the hydrostatic equilibrium of a box in heave and pitch, comparing the solution given by the linear and nonlinear approximations.

We consider a box with the following dimensions \((L,B,H) = (8,4,2)m\), with a center of gravity located at the center of the box. Its mass is taken as

\[mass = \dfrac{1}{2} \rho_{water}\times V_{box} = \dfrac{1}{2} \rho_{water}\times L \times B \times H\]

An artificial linear damping force is introduced, to make for the hydrodynamic radiation damping. (see Damping force). The diagonal coefficients are taken at \(1E4\) for the translation and rotation degrees of freedom.

decay test in heave, in small amplitude motions

Fig. 24 Decay test in heave, in small amplitude motions : blue = linear approximation, orange = nonlinear approximation

decay test in heave, in large amplitude motions

Fig. 25 Decay test in heave, in large amplitude motions : green = linear approximation, red = nonlinear approximation

decay test in pitch, in small amplitude motions

Fig. 26 Decay test in pitch, in small amplitude motions : violet = linear approximation, brown = nonlinear approximation

decay test in pitch, in large amplitude motions

Fig. 27 Decay test in pitch, in large amplitude motions : pink = linear approximation, grey = nonlinear approximation