Modeling of Response Amplitude Operator for Coupled Sway, Roll and Yaw Motions of a Floating Body in Sinusoidal Waves Using Frequency Based Analysis

The paper investigates the characteristics of response amplitude operators (RAO) or transfer function of a floating body in frequency domain for coupled sway, roll and yaw motions in sinusoidal waves. The floating body is considered to be initially at rest and waves act as beam to the floating body with varying frequency (⁠$ω$⁠) between 0.3 rad/s and 1.2 rad/s. The hydrodynamic coefficients (HC) are computed using strip theory formulation and the general expression of RAO is derived. The behavior of RAO under coupled conditions is examined by considering two asymptotic cases, corresponding to $ω→0$ and $ω→∞$⁠. For the intermediate frequency range, analytical expression for system frequency is derived. The effects of viscous damping for uncoupled and coupled transfers have been compared with the result of nonviscous case. A mathematical analogy with respect to Mathieu and Hill equations has been established using frequency based classifications of governing equations. This modeling approach can provide useful guidelines to determine RAO for coupled motions and computing of wave loads and sensitivity analysis with respect to initial conditions of a floating body for the wide range of frequencies.