A Time Series Model for Dynamic Behavior of Offshore Structures
Authors: Burke Ben G. , Tighe James T. 
Published: December 2007

Abstract
An analytical model is presented for evaluating the dynamic behavior of offshore structures subject to earthquake and storm wave forces. A mathematical model is formulated as a system of nonlinear differential equations that are solved by direct numerical integration on a digital computer. The offshore structure is represented in the model by a lumped mass system with linear stiffness and damping characteristics. Nonlinearities arise from the representation of hydrodynamic forces on the structure by the Morison equation, with velocities and accelerations based on the relative motion between structure and water.
Random wave forces are obtained from wave velocities and accelerations simulated from a Pierson-Moskowitz wave spectrum. Earthquake Pierson-Moskowitz wave spectrum. Earthquake excitation consists of a time history of horizontal base accelerations obtained from actual or simulated earthquake accelerograms. Results are presented in the form of root mean square (rms) values, maximum amplitudes, and power spectra for nodal deflections and accelerations, base shear and overturning moment.
Results from the analysis of four prototype structures in water depths of 400 to 1,000 ft showed: (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 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 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 have been reported.
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. For example, the model includes an exact representation of the square-law, hydrodynamic drag force and 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 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 presents the results of analyses of four deepwater platforms to demonstrate the significance of dynamic platforms to demonstrate the significance of dynamic behavior and to show the importance of including structure motion in the hydrodynamic force equation.