Abstract
In this work, the response of a ship rolling in regular beam waves is studied. The model is one degree of freedom model for nonlinear ship dynamics. The model consists of the terms containing inertia, damping, restoring forces, and external forces. The asymptotic perturbation method is used to study the primary resonance phenomena. The effects of various parameters are studied on the stability of steady states. It is shown that the variation of bifurcation parameters affects the bending of the bifurcation curve. The slope stability theorems are also presented.
Highlights
In ship architecture, ship-roll motion is the oscillatory motion of a ship along its longitudinal axis
Maccari applied the asymptotic perturbation method to study the nonlinear dynamics of a third order ordinary differential equation obtained by traveling the wave solution of a Burgers–KdV type equation [38]
Under primary resonance 1:1, the authors study the response of system varying different system parameters
Summary
Ship-roll motion is the oscillatory motion of a ship along its longitudinal axis. Ship-rolling models in a single degree of freedom and nonlinear damping can be traced back to the work of Froude [3]. The work of Kreuzer and Wendt [14] considered nonlinear ship dynamics with six degrees of freedom and presented simulations of a realistic ship behavior in waves during capsize and showed the importance of the nonlinearities of the mathematical model. In [24], the authors used methods of multiple time scales and considered linear, quadratic, cubic, and quintic terms of roll angle. They used Lyanopnov’s first method in their investigation to show the effects of different parameters of the system. We will discuss a ship roll model from [24] using the Asymptotic Perturbation method
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