Diffraction method for spar platforms

Abstract
This paper presents the numerical hydrodynamic analysis for the motion responses of spar offshore platforms in regular sea waves using both Morison Equation and Diffraction Method. The spar was modeled as a rigid body with three degrees of freedom restrained by mooring lines affecting the stiffness values. Linear Airy wave theory and Morison’s equation were used for calculating the wave forces on the
structure in the first case. The mass, damping and stiffness matrices were evaluated at every time step and
the equations of motion were formulated for the platform dynamic equilibrium. The equations were solved
using Newmark’s Beta time domain dynamic analysis method. The results were obtained as Transfer Functions in Surge. In the second case, the Transfer Functions were obtained using a linear diffraction Method. The results were compared and conclusions arrived at. It was observed that the responses using diffraction method were higher than that using Morison Equation for the low frequencies and vice versa for the high frequency.
Keywords
Spar platforms, Hydrodynamic analysis, Degree of freedom (DOF), Morison modified equations,
Diffraction method, and Transfer function.