A Time Series Model for Dynamic Behavior Of Offshore Structures
Authors: Burke Ben G. , Tighe James T. 
Published: October 2008

ABSTRACT
The design of platforms for deep water requires an understanding of the dynamic behavior of the structure during earthquakes and storm wave conditions. This paper presents results of an analytical study on evaluating dynamic response. The offshore structure is represented by a mathematical model that reduces to a system of nonlinear, differential equations that are solved by direct numerical integration on a digital computer. The structure is represented by a lumped parameter system of discrete masses on a network of stiffness elements. Structural damping is determined from assigned modal damping ratios in air. Structural parameters are based on actual preliminary designs for four structures in water depths of 400 to1,000 feet. The hydrodynamic forces on the structure are computed from the Morison equation, with velocities and accelerations based on the relative motion between structure and water. Wave velocities and accelerations are simulated from a Pierson-Moskowitz have spectrum by a random sea model. Earthquake excitations consist of horizontal base accelerations obtained from simulated earthquake accelerograms. Results are represented as rms values, maximum amplitudes and power spectra for deck defleaction, base shear and overturning moment. The analysis of the four structures showed that (1) dynamic response to waves is significant for structures with a fundamental natural period greater than approximately 2.4 seconds, (2) including relative water-structure motion in the Morison force equation contributes significantly to damping of structural vibration, and (3) the statistical nature of extreme values for structural response to waves is not adequately described by the commonly assumed Rayleigh distribution.

INTRODUCTION
Engineering practices for most offshore drilling platforms built to date have been based on static analysis methods. Such methods provide adequate designs because the resulting structures are relatively stiff with fundamental periods of vibration below the range of significant wave energy. However, the recent of significant wave energy. However, the recent interest and activity in deeper water development has emphasized the need for investigating the potential dynamic behavior of offshore structures. A number of analysis techniques are reported in the literature, most of which can be broadly classified as spectral, or frequency domain, methods. The results of some of these investigations are reported in References 1-6. The model developed in this paper is based on a time domain approach, in which the dynamic behavior of an offshore structure subject to wave or earthquake forces is studied sequentially in time. The advantage of this approach is that nonlinear functional relationships, which require approximations in the spectral models, can be handled exactly in the time domain. For example, the model presented here includes an exact representation of the square-law hydrodynamic drag force the additional effect of relative water-structure motion in the drag force equation. The paper is presented in two parts. Part I presents the mathematical model of the structure in waves and earthquakes and describes its implementation on a digital computer. Part II presents the results of analyses of four deepwater platforms to demonstrate the significance of dynamic behavior and to show the importance of including structure motion in the hydrodynamic force equation.