Abstract

Accurate estimates of damping are of critical importance in the design of large offshore platforms susceptible to fatigue damage. Two damping mechanisms are discussed which are related to the interaction between the structure and the flow. Wave radiation damping results from the propagation of energy away from the structure by motion-induced waves. A reciprocity relationship is used to estimate the magnitude of wave-radiation damping based of the force from incident waves. Separated flow damping is generated by the flow separation past the tubular members forming the framework of the structure. A mathematical model of the problem is created which is applicable to a structure of arbitrary complexity within a random wave field. Arguments based on the average rate of energy dissipation and the method of Gaussian closure are used to estimate the damping from this source. A method for estimating the response of a resonant system to random waves is introduced which does not require direct computation of the exciting force. Rather, the response is related to the ratio of the wave-radiation damping to the total damping. The ratio of the separated-flow damping to the wave-radiation damping is computed for one simple geometry. Estimated response is compared against measured response for a model of this geometry which was tested.

Introduction

One of the considerations in the design of a large steel offshore structure, such as an oil production platform, is fatigue. The main culprit in fatigue failure of an offshore structure is the large number of stress cycles to which the structure is subjected by moderate sea states. For the largest oil production platforms, resonant amplification of the response in the vicinity of the lowest natural frequencies of the structure can make an important contribution to the total response in moderate seas. In the vicinity of a natural frequency of the structure, the response is strongly influenced by the damping of the resonating mode. The major damping terms include internal damping due to hysteresis, damping due to energy dissipation into the seabed and hydrodynamic damping. Within the latter category, potential flow theory can be used to predict a waveradiation damping[l]. In addition, a number of researchers[2,3] have shown the existence of a second damping term which is related to the separation of flow past the cylindrical sections forming the underwater portion of a typical oil production platform. The objective of this paper is to develop and apply formulae to predict the magnitudes of the two hydrodynamic components to the damping. A method will be introduced for describing the underwater geometry of a general offshore platform consisting of a number of cylindrical sections. The flexural motions of the structure will be expressed in terms of the modal motions. The modal hydrodynamic force in an inviscid flow will be derived and used with a reciprocity relationship between excitation force and damping to estimate the wave-radiation damping of a mode. The hydrodynamic force in a viscous fluid will be modelled by a relative velocity formulation of Morison's equation[4].

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