Abstract

An exact second order solution is presented for the slowly varying drift overturning moment on an articulated column in irregular waves. The wave diffraction problem is formulated and solved correctly to second order in wave amplitude by application of Green's second identity and Haskind's reciprocal relations. The approach allows the evaluation of the second order excitation force due to the second order wave without knowing the second order pressure distribution over the body surface. All the contributions to the total drift moment are thus evaluated only from the solution to the first order diffraction problem, for which explicit analytical results are available. As illustration of the theory, results are presented for the quadratic transfer functions of the drift overturning moment, which are then used to investigate the slow drift motion of the articulated column under typical sea conditions. The present exact results are also compared with those from different simplified solutions. Conclusions arising from these numerical results may be summarised as follows : a) In short to moderate seas with high wave frequencies, the total drift moment is dominated by the force components arising from products of first order quantities. In this frequency range, the slowly varying drift moment may be predicted fairly well with the knowledge of the mean drift moment in regular waves ; b) In extreme seas with longer wave frequencies, the component from the second order locked wave dominates the total slowly varying drift moment. In such low frequency range, diffraction effects due to the first order wave are so small that the contribution of the second order wave may be calculated most accurately by means of the proposed approximate method neglecting these effects ; c) The conventional method using data of the mean drift moment in regular waves gives accurate results for the slowly varying moment in short to moderate seas, but tends to underestimate the responses in extreme sea state with longer mean wave period.

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