Dynamics of Ship–Motion

Abstract

The ship capsizing problem is one of the major challenges in naval architecture. The Current stability criteriaCurrent stability criteria are based on static assumptions. The roll-restoring moments, called righting moments in calm water, are calculated at various heeling angles. By dividing the righting moment by the weight of the ship the righting lever curves, Figure 1, are obtained. The slope of the righting lever curve at 0• is called initial stability or metacentric height GM . National and international rules on intact stability -which consider non-damaged-ships -make demands on minimum values and characteristics of these curves [1]. The rules require a minimum area of the righting lever curve between 0• and 30• and between 0 • and 40• , the minimal size of the righting lever at 30 • , the minimum metacentric height at 0• , and that the maximum righting lever has to lay at 25 • or higher.Model tests and practical experience show that the current stability criteria do not always correspond to the danger of capsizing. Large-amplitude motions, which neither can be predicted accurately by static criteria nor by linear theory are associated with nonlinear dynamic effects. Consequently, we propose to develop a criterion taking these nonlinear effects into account. Mathematical modelConsider that a ship freely floating in regular waves can be considered as a rigid body with six degrees of freedom. The equations of motion are obtained from the principle of linear and angular momentum. Denoting the position vector of the center of gravity with respect to the space-fixed frame with r CG and the ship's angular velocity with omega one obtains in coordinates of the body-fixed frame K S : {CG, x S , y S , z S }, Figure 2:where m is the mass of the ship, S J is the 3 × 3 inertia matrix with respect to CG and K S , S f and S m are the vectors of applied forces and moments acting on the ship due to radiation and diffraction, head and beam resistance,

Results from Bifurcation Analysis in Ship Dynamics

“…The hydrostatic forces are calculated fully nonlinear, the calculation of the hydrodynamic forces bases on the strip theory for instationary flows. Two capsize scenarios have been found previously [4] and show the importance of a nonlinear analysis. With the applied method dangerous and non-dangerous regions of ship operations can be determined.…”

“…When describing hydrodynamics, the history of the flow is very important for calculating the actual state of the flow [2], so a system of integro-differential-equations is needed for the further bifurcation analysis. Two kinds of capsize scenarios were detected [4] and it can be shown that increasing wave-height does not always lead to increasing roll amplitudes. This indicates the importance of the usage of full dynamical models in stability analysis of floating structures.…”

“…For comparision of experiments and simulation with the model described in [4] the data of three model tests with different forward speeds were chosen and simulations with adequate parameters were done. In Figure 1 a phase plot of the roll motion measured during the experiments (left side) and a phase plot of the roll motion obtained by simulations (right side) is shown.…”

Innovative Solution for Harvesting Energy in Marine Vessels

“…The electromagnetic subsystem is inducing current i, and L is inductance, R is electrical resistance, where Rc is coil resistance and Rd is load resistance, and R = Rc + Rd. The VEHD dynamics is described by system of ordinary differential equation (see [7][8][9][10][11], [14,15]) J```c +m 2 (-x/r) + b1(`-x`/r) = sin ( t) (1) mx``-m 2 (x/r) -b1(`-x`/r) + mi = 0 (2) Li`+ Ri -ex`-r`= 0 (3) where `=d/dt, m is the linkage factor between mechanical and electromagnetic subsystems in mechanical terms, e is the linkage factor between electromagnetic and mechanical subsystems in electromagnetic terms, and r is the distance from a centre of vessel mass to VEHD location.…”

“…The marine vessels are experiencing different types of dynamic loads during operation [1,2]. One of the results of dynamic loads is the various kinds of vessel's oscillations.The authors selected one type of oscillations known as "pitching" for study in that paper.…”