ABSTRACT

The stochastic dynamic responses of offshore platforms, with and without the presence of current, are studied and discussed the formulation derived in the paper can be used to determine the statistics of platform response with proper consideration of the nonlinear effect caused by current. The phenomenon of wave-current interactions is known to change wave characteristics; its effect on structural responses is also examined.

Five deepwater platforms are analyzed under different wind wave and current loading conditions. Numerical results showing the effect of current, the contribution of current when the wind waves become stronger, and the effect of wavecurrent interactions on the dynamic response are presented.

INTRODUCTION

As the design of offshore platform moves into deeper water, dynamic excitation becomes an important factor. The dynamic behavior of fixed platforms to random waves or earthquakes has been studied in several papers. I - 4 Usually the wave forces exerted on members of the structure are computed according to Morison's formula. 5 That is, forces are considered to consist of two parts:

  1. the drag force, proportional to the square of fluid particle velocity, and

  2. the inertia force, proportional to fluid particle acceleration. When the current exists in the platform location, the total fluid particle velocity should be considered as the vector sum of current velocity and wave-induced fluid particle velocity. Since the drag force is nonlinearly related to fluid particle velocity, it cannot be regarded as a simple superposition of current and wave drag forces. 0 Therefore, new formulations and derivations are required to calculate the dynamic responses of platforms due to combined actions of current and waves.

Small amplitude wave theory is used and effects of fluid-structure interactions12,13 are considered in this study. The nonlinear stochastic differential equations of structural response are solved by the equivalent linearization technique to allow the use of the normal mode superposition method. A computer program has been developed for practical application of this analytical approach. Five deepwater platforms are analyzed for various wave and current conditions. The Pierson-Moskowitz wave spectrum is used to describe the random waves, and the platforms are assumed to respond in the linear elastic range numerical results are presented to show the importance of including currents in the dynamic analysis.

EQUATIONS OF MOTION

The fixed offshore platform is idealized as a lumped mass system as shown in Figure 1. The equations of motion of the N degrees of freedom system can be written in matrix form as

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