Approximate analytical investigation of large-amplitude rolling motion of ships with the improved Galerkin method

Abstract

In this study, the large-amplitude rolling motion of a ship was studied. First, the harmonic balance method was used to construct a reasonable initial approximate solution. Subsequently, the Newton linearization and Galerkin method were combined to obtain the analytical approximate solution of the ship's large-amplitude roll motion. By comparing with the numerical solution, the accuracy of the analytical approximation solution was verified. The results showed that the third-order analytical approximation had a higher accuracy for small and large amplitudes. Based on the analytical approximate solution, the influence of nonlinear quadratic damping and nonlinear restoring moment on the global stability of the ship under different amplitudes was analyzed. The theoretical results can guide the design and stability analysis of large rolling motions of ships.