Analytical Model to Determine Response Amplitude Operator of a Floating Body for Coupled Roll and Yaw Motions and Frequency-Based Analysis

The paper deals with the mathematical modeling of response amplitude operator (RAO) and frequency-based analysis for coupled roll and yaw motions in regular waves. Prior to obtaining the RAO expressions for linearly coupled conditions, hydrodynamic coefficients are computed by using the strip theory formulation. We consider sinusoidal wave with frequency (ω) varying between 0.3 rad/s and 1.2 rad/s acts on beam to the floating body for zero forward speed. Two limiting cases corresponding to ω → 0 and ω → ∞ are considered and general expressions of RAO for intermediate frequencies are derived. Analytical result shows that the norm of RAO is maximum when ω ≈ ωn≈ 0.74 for coupled roll and yaw motions. The asymptotic convergence of real part, imaginary part and norm of uncoupled yaw transfer functions are noticed with the increase of wave frequency. Using the normalization procedure and frequency based analysis; group based equations are formulated for each case. To understand the relative importance of the hydrodynamic coefficients, analytical solutions are obtained. The sensitivity analysis with respect to the initial conditions is investigated for roll and yaw motions. This study could be useful to model the floating body dynamics and corresponding wave loads in the design stage.