This paper deals with the dynamical analysis of a vessel that leads to capsize in regular beam seas. The complete investigation of nonlinear behaviors includes sub-harmonic motion, bifurcation, and chaos under variations of control parameters. The vessel rolling motions can exhibit various undesirable nonlinear phenomena. We have employed a linear-plus-cubic type damping term (LPCD) in a nonlinear rolling equation. Using the fourth order Runge-Kutta algorithm with the phase portraits, various dynamical behaviors (limit cycles, bifurcations, and chaos) are presented in beam seas. On increasing the value of control parameter Ω, chaotic behavior interspersed with intermittent periodic windows are clearly observed in the numerical simulations. The chaotic region is widely spread according to system parameter Ω in the range of 0.1 to 0.9. When the value of the control parameter is increased beyond the chaotic region, periodic solutions are dominant in the range of frequency ratio Ω=1.01~1.6. In addition, one more important feature is that different types of stable harmonic motions such as periodicity of 2T, 3T, 4T and 5T exist in the range of Ω=0.34~0.83.

Abstract
 1. Introduction
 2. Mathematical Formulation
  2.1 System description
 3. Simulation Tests
 4. Conclusions
 References

• Sang-Do Lee(Graduate School of Korea Maritime and Ocean University, Busan, Korea)
• Sam-Sang You(Division of Mechanical Engineering, Korea Maritime and Ocean University, Busan, Korea) Corresponding Author