4.4 Seakeeping analysis

In the design of ships and ocean structures, the wave-induced motions are of great importance to the assessment of the comfort and safety of the crew and the passengers.

Seakeeping analyses should be performed to estimate seakeeping ability or seaworthiness, that is how well-suited a marine craft is to conditions when underway.

Harmonic oscillator without forcing

$$\ddot{z}+2\zeta {\omega }_n\dot{z}+{\omega }_n^{2}z=0$$ $$\ddot{z}+d\dot{z}+kz=0$$

For ships we add waves as forcing.

Solution (no forcing):

$$z(t)=A{e}^{\zeta {\omega }_{n}t}\sin (\sqrt{1-{\zeta }^2}{\omega }_{n}t+\varphi )$$

Natural frequency (undamped angular frequency):

$${\omega }_n=\sqrt{\frac{k}{m}}$$

Relative damping ratio:

$$\zeta =\frac{d}{2\sqrt{mk}}$$

Harmonic oscillator with sinusoidal forcing

Steady-state heave, roll and pitch responses in regular waves