Polyharmonic Balance Analysis of Nonlinear Ship Roll Response

A recently developed analytical algorithm for generating thepolyharmonic balance equations of a class of nonlinear differentialequations has been used to perform a detailed four-component analysis ofa single-degree-of-freedom ship roll model with cubic damping andquintic stiffness terms subject to a biased sinusoidal forcing function.The tradeoff between accuracy and complexity has then beensystematically investigated across a range of input sinusoidalfrequency, amplitude, and input bias, by investigating the effect ofneglecting harmonic or model terms in the more detailed analysis andthen comparing the results to independent solutions obtained throughdirect numerical integration of the governing equation.