ABSTRACT

Theoretical calculations show that large tendon loads can be induced by the resonant pitch response of a TLP when exposed to waves that have a period that is twice the natural pitch period of the TLP. To verify the theoretical predictions, two model test programs, one measuring "springing" forces on a large-diameter (4 ft) vertical cylinder and the other measuring the response of a large-scale (l: 16) tension leg platform, were carried out in 1984 in the CBI Industries, Inc., wave tank in Plainfield, Illinois. Regular, paired, and random waves were used. Results confirm that "springing" forces exist, hydrodynamic damping is very low, and second-order diffraction theory yields fair to good predictions.

INTRODUCTION

Studies carried out by Chevron indicated that "springing" forces (second-order forces that occur at a period that is one-half the wave period) could be an important consideration for the design of tension leg platform (TLP) tendons against fatigue damage. Although the magnitude of these forces was predicted to be very small, theoretical calculations showed that the hydrodynamic damping is also extremely small. Consequently, it was concluded that large tendon loads could be induced by resonant pitch response of the TLP.

The objectives of the test programs were to:

  • test the existence of springing forces,

  • estimate hydrodynamic damping,

  • evaluate predictability of the response using second-order diffraction theory, and

  • assess importance of springing for design.

The paper presents:

  • comparisons between measured and predicted regular-wave springing forces on the vertical cylinder,

  • comparisons between measured and predicted TLP response for regular and random waves,

  • hydrodynamic damping estimates, and

  • sample time-histories and spectra of the TLP tendon loads.

The paper also compares Chevron's independently obtained theoretical predictions with those published by Herfjord and Nielsen (1986). Chevron's prediction method for springing forces was developed by Prof. D. K. Yue of MIT while consulting on TLP response calculation methods.

The information provided in the paper can be used to assess the importance of springing to TLP tendon design and the usefulness of second-order diffraction theory for predicting the response.

SOURCE OF SPRINGING FORCES

An intuitive appreciation for the source of springing forces can be gained by examining Figure I, which shows the effect of integrating a uniform, local horizontal force, f = A cos wt, up to the water surface, yet(t) = A cos wt. This results in a total force that includes a second harmonic whose amplitude is proportional to the square of the wave amplitude. This component of the total force, the springing force, induces a moment on the TLP which then can excite the structure in pitch resonance. The excitation would be provided by a wave whose period is twice the natural pitch period.

A rigorous representation of the springing force, based on potential theory, can be obtained through a perturbation solution of Laplace's equation with the nonlinear kinematic and dynamic free-surface boundary conditions, and the no-flow boundary condition on the body. Such a solution has been obtained by Chevron and has also been obtained and published by Herfjord and Nielsen.

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