Analytical solution of nonlinear rolling motion of ship using the method of multiple scales

In this research, the nonlinear rolling motion of ships is studied. After obtaining the governing equation of roll motion, the method of multiple scales perturbation technique is applied to solve the nonlinear differential equation. The ship response is studied with and without harmonic excitation. In order to validate the responses obtained by the method of multiple scales, the response was compared with the numerical solution. Finally, the effects of damping coefficient and restoring arm on the frequency response function and resonance frequency have been studied.