Dynamic responses of classic spar platforms subjected to long crested waves: Morison equation vs. Diffraction theory

Morison equation, Froude Krylov theory and Diffraction theory are the common theories used to evaluate the wave force for offshore structures. The applicability of these theories is based upon the type and size of the member of the structures. Morison equation is normally used for small structures compared to wave length, while for large structures Diffraction theory needs to be applied. However, in many cases Morison equation has been used to obtain the wave forces for classic spars, which are large offshore structures installed in deepwater. This paper presents the results of numerical investigation of an offshore classic spar platform subjected to long crested waves. Two numerical simulations were developed by incorporating the Morison equation and Diffraction theory to obtain the wave forces. The classic spar was modeled as a rigid body with three degrees of freedom restrained by mooring lines. In the simulation, the mass, damping and stiffness matrices were evaluated at every time step. The equations of motion were formulated for the platform dynamic equilibrium and solved by using Newmark Beta method. The results were obtained in terms of Response Amplitude Operator (RAO) for surge, heave and pitch motions. The dynamic responses obtained were compared.