Dynamic Responses of Classic Spar Platforms Subjected to Long Crested Waves: Morison Equation vs. Diffraction Theory

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.
Keywords-Classic spar, Morison equation, Diffraction theory,
Response Amplitude Operator (RAO).