Park, Han Il; (1992) Dynamic stability and vibrations of slender marine structures at low tension. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis describes an analytical and numerical investigation into the dynamic behaviour of long slender structures under forcing, parametric and combined periodic excitations as well as under pulse loading. In particular, this work is directed at obtaining an understanding of the dynamic stability and vibrations of slender vertical marine structures at low tension with applications to the tethers of tension leg platforms (TLPs) and to vertical marine risers. A closed form solution for exact natural frequencies and corresponding mode shapes of slender vertical cylinders is obtained analytically by using the Bessel function. This is followed by analysis to obtain the response of such structures when subjected to lateral forces (forcing excitation). This is done by reducing their governing partial differential equation to a non-linear differential form by applying Galerkin's method and the method of separation of variables. This non-linear equation is then solved analytically and semi-analytically to obtain forced vibrations of the structure. When slender marine structures are subjected to a time-varying axial force, they can exhibit parametric vibrations described by the Mathieu equation. The Mathieu stability chart over such a wide range of parameters is obtained. In addition, a non-linear Mathieu equation for the lower-order instability regions is analytically solved by using a perturbation method. In order to solve the equation of the higher-order instability regions, a fourth-order Runge-Kutta method is employed. In reality, most slender marine structures such as tethers of TLPs are subjected to both time-varying axial forces and lateral forces giving rise to combined parametric and forcing excitation. This combined excitation is solved to demonstrate that the effect of combined excitation on the response of such structures becomes significant compared to forcing or parametric excitation, especially in the even numbers of instability regions for the Mathieu chart. For the same excitation strength, the response amplitude of the structures under combined excitation is found to be the largest in the second instability region. In order to deal with the dynamic stability of slender vertical structures at low tension in the higher-order instability regions, dynamic pulse buckling is also investigated. It is known that if the load duration is short enough, long slender marine structures can survive axial loads much larger than the static Euler load value. In this work, the theory of dynamic pulse buckling is applied to rather short TLP tethers in order to obtain confirmatory criteria for allowable compressive axial load and its duration time. A finite element method with a time-varying stiffness matrix is used to verify analytical results. Results from the finite element method are in good agreement with analytical results. The results of the above theoretical developments are illustrated by application studies on a marine riser and the tethers of three conventional TLPs - on the Hutton, Jolliet and Snorre fields. It is found that the effect of combined excitation is significant on the dynamic behaviour of the tethers at low tension and that the conventional high pretension of their tethers can be reduced to a certain extent.

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