Technical NoteNumerical simulation of ship stability for dynamic environment
Introduction
Stability against capsizing in heavy seas is one of the fundamental requirements in ship design. Capsizing is related to the extreme motion both of ship and waves. Rolling of a ship in rough environment may be influenced by many factors. They can be divided into three main situations; beam sea, following and quartering sea conditions. In the present study, the problem of ship safety has been studied with regard to the rolling motion of a ship in beam waves.
Bhattacharyya (1978) discussed rolling motion of a ship and the devices for roll damping. Dalzell (1978) discussed about the representation of damping in different nonlinear forms. Odabasi and Vince (1982) concentrated on the roll response of a ship under the action of sudden excitation. They studied the importance of roll damping on the response of a ship. Vassalos et al. (1985) explained stability criteria for semisubmersible stability. Lewis (1988) concentrated on rolling dynamics taking into account the wave and other environmental effects. Witz et al. (1989) investigated the roll response of a semisubmersible model with an inflectional restoring moment. Zborowski and Taylan (1989) studied the small vessel’s roll motion stability reserve for resonance conditions. De Kat and Paulling (1989) investigated motions and capsizing of ships in severe sea conditions. Francescutto (2000) studied the problem of ship safety with regard to the stability and rolling motion of ships in beam waves. Taylan (2000) investigated the effect of nonlinear damping and restoring in ship rolling. Chakrabarti (2001) explained various types of damping associated with rolling. He contributed empirical relationships for the calculation of roll damping.
Section snippets
Formulation of the problem
For the purpose of analysis, only the significant motion pertaining to stability and capsizing, namely roll motion has been considered. This simplification can be justified by the reasoning that the vessel capsize is strongly influenced by the roll motion. In addition, among the three transverse coupled motions, only roll has restoring forces and exhibits strong resonant motions. Hence, roll motion can be considered to be the most important in the stability analysis of a vessel.
The factors that
Results and discussions
For the purpose of analysis of linear and nonlinear rolling motion of ships, two vessels that differ in hydrostatic and stability characteristics have been considered. Fig. 1, Fig. 2 show the body plan and isometric view of a RO–RO ship. Table 1 shows the principal particulars of a RO–RO ship. The stability characteristics of the RO–RO ship, viz. GZ, GM, vanishing angle of stability and area under GZ curve are determined by well known Krylove’s method. Fig. 3 shows the GZ curve obtained based
Conclusions
Analytical methods are formulated for the roll motion of ship. Linear and nonlinear approaches are tried. Solutions are obtained using the fourth order Runge–Kutta method. Three types of possible damping are considered based on the literature survey. The restoring arm curve is represented by quintic polynomial. The result of the present approach very well agrees with the published results. A number of cases have been worked out.
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