Nonlinear vibration analysis of the large-amplitude asymmetric response of ship roll motion

Ship roll motion is the single most important factor responsible for ship capsizes. Yet, there is still much to be understood about this subject; especially, how critical parameters influence the asymmetric response during large initial roll amplitudes. Consequently, this paper presents an investigation of the nonlinear vibration of the large-amplitude asymmetric response during ship roll motion. The dynamic model governing the roll motion accounted for quadratic damping and cubic nonlinear restoring moment with softening behaviour. The continuous piecewise linearization method was adopted to solve the governing model. Hence, the effect of four critical parameters (i.e. initial roll amplitude, added mass, quadratic damping and nonlinear restoring moment) on the asymmetric roll response and capsize tendency was investigated. It was observed that capsize tendency was strongly linked to the offset of the equilibrium point and the asymmetric response, which amplified the initial roll amplitude. An increase in the initial roll amplitude or quadratic damping produced a stronger asymmetric response and an increased capsize tendency, while an increase in the added mass or nonlinear restoring moment weakened the asymmetric response and decreased the capsize tendency. Also, an increase in any of the four critical parameters produced a decrease in the frequency of vibration.