文档介绍：Ocean Engineering 31 (2004) 2175–2208
ate/oceaneng
Mathieuinstability of a spar platform
with mooring and risers
. Koo, . Kim Ã, . Randall
Ocean Engineering Program, Civil Engineering Department, Texas A&M University,
College Station, TX 77843-3136, USA
Received 27 November 2003; accepted 24 April 2004
Abstract
Mathieuinstability for a spar platform arises when there is a harmonic variation in the
pitch restoring coefficients caused by large heave motion and the period of the heave motion
is half of the pitch natural period. The pitch restoring coefficient can be represented by a
function of the displaced volume and the metacentric height of spar hull. Due to heave
motion, the displaced volume and the metacentric height of the spar platform change in time
and this heave/pitch coupling can be represented by Mathieu’s equation. The objective of
this study is to evaluate damping effects and hull/mooring/riser coupled effects on the prin-
cipal instability. In the simulation, the heave/pitch coupling of the spar platform is con-
sidered using the modified Mathieu equation. The wave elevation effect on Mathieu
instability is also investigated. The Mathieuinstability of a practical spar platform is care-
fully checked by a series of systematic simulations parisons of many different sce-
narios. When heave resonance occurs at the heave natural period equal to half of the pitch
natural period, Mathieu instability, a kind of lock-in phenomenon, actually arises to increase
the pitch motion significantly. The available damping is found to be important in suppres-
sing the instability. The results also show that the additional pitch restoring force from
buoyancy-cans plays an important role in the spar Mathieu instability.
# 2004 Published by Elsevier Ltd.
Keywords: Spar platform; Mathieuinstability; Heave–pitch coupling;Time-varying pitch restoring coef-
ficient; Hull–mooring–riser coupling; Damping and wave-elevation effect
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