计及平台运动响应谱的顶部张紧立管稳定性曲线研究

摘要

针对顶部张紧立管在不规则波作用下可能会失稳的问题，研究了计及平台运动响应谱的张紧立管稳定性曲线。首先计算出了张力腿平台的运动响应谱，依据该运动响应谱的特性，将不规则波波浪作用下张力腿平台的运动响应以一系列规则波叠加的形式给出。并将这一系列的规则波输入到顶部张紧立管的参激振动方程当中。同时，采用伽辽金法简化控制方程，得到参激振动的马蒂厄方程。最后，利用小参数法对其进行推导，得出了顶部张紧立管的稳定性曲线公式。研究结果表明：平台运动响应谱对顶部张紧立管的稳定性曲线有着很重要的影响。%Regarding the problem of the potential instability of the top tension riser under irregular wave action, we obtained stability curves for the top tension riser under the effect of the platform's motion response spectrum. First, we calculated the motion response spectrum of the tension leg platform. Based on the features of the motion response spectrum, we superimposed the motion response of the tension leg platform on a series of regular waves. The regular wave series were then input into the top tension risers' parametrically excited vibration equation. By applying the Galerkin method, we simplified the control equation and obtained the parametrically excited Mathieu equation. Fi⁃nally, we obtained the stability curve equations of the top tension riser by deducing the small parameters. The re⁃sults prove that the platform's motion response spectrum is vital to the stability of the top tension riser.