Dynamics of tension leg platform tethers at low tension. Part I - Mathieu stability at large parameters
| Autor: | H.I. Park, Minoo H. Patel |
|---|---|
| Rok vydání: | 1991 |
| Předmět: |
Engineering
Partial differential equation Tension (physics) business.industry Oscillation Mechanical Engineering Ocean Engineering Particle displacement Mechanics Instability symbols.namesake Classical mechanics Mathieu function Mechanics of Materials symbols General Materials Science business Tension-leg platform Parametric statistics |
| Zdroj: | Marine Structures. 4:257-273 |
| ISSN: | 0951-8339 |
| DOI: | 10.1016/0951-8339(91)90004-u |
| Popis: | The tethers of tension leg platforms have conventionally been designed to have sufficiently high pre-tension so as not to go slack in extreme conditions of low tide levels and high waves. The high tether pre-tension necessary for this is found to be a significant restriction to the payload increase over conventional design that is needed for an operational platform. This paper reports on the first stage of an investigation into the dynamics of tethers with reduced pre-tension to facilitate payload increase over conventional design of a TLP. When tether pre-tension is reduced, the wave-induced time-varying axial force becomes important in its dynamics. This time-varying axial force causes the tether to undergo parametric oscillations described by the Mathieu equation. Fortunately, in the case of a tether, even if it is in an unstable condition, the quadratic fluid damping force limits the amplitude of the lateral motion. However, the limited amplitudes vary according to the combination of the Mathieu parameters. Therefore, it is necessary to obtain the Mathieu stability chart up to the large parameters which can arise for tethers at low tension. The governing partial differential equation is derived for lateral motion of a tether and reduced to the nonlinear Mathieu equation. The Mathieu stability chart is obtained over a wide range of parameters. In addition, the steady-state solutions of oscillation in the first instability region are obtained analytically. In order to obtain the solutions in higher-order instability regions, a numerical method is employed. The results show that even if tether is in a slack condition, the displacement amplitude of parametric oscillation is not large for some dimensions. Therefore, it is possible to reduce the high pre-tension of tethers in terms at least of excitation of parametric tether oscillations. |
| Databáze: | OpenAIRE |
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