Dynamic Analysis Of Plane Mooring Chains Of Inextensible Links.

Abstract

In this paper the dynamic problem of inextensible chains is addressed. Chains and cables
are employed as mooring devices as well as in other structural applications. The dynamic response of
structural elements (e.g. floating platforms) joined to the chains/cables are influenced by the strong nonlinearity
which is of the geometric rather than any material type. The nonlinear Differential-Algebraic
Equations (DAE) are derived by direct dynamic equilibrium. The chain may be subjected to general
loads. It is also considered that both ends can undergo arbitrary dynamic displacements. The ordinary
DAE are tackled by means of temporal power series. It is worthwhile to mention that the explicit expansion
in the time variable leads to a linear algebraic system in the series coefficients for each power
of t, despite the strong nonlinearity of the system. The consequent advantage is the availability of an
analytical solution that allows the validation of other numerical solutions. The algorithm is illustrated
by numerical examples in which the chain is subjected to self-weight with one end fixed and the other in
prescribed motion. The different trajectories of the chain dynamic response are presented. Any number
of links may be considered and taking a large number of links gives place to an inextensible cable model.