水下悬浮隧道锚索稳定性分析

Stability analysis of submerged floating tunnel tether

为研究水下悬浮隧道锚索的稳定性，建立锚索在涡街激励作用下振动的数学方程，采用伽辽金法对其进行化简，锚索振动的稳定性通过 Lyapunov 指数法进行判断，分析了锚索动静张力比的大小、悬浮隧道系统的阻尼比和锚索参数激励频率对锚索振动稳定性的影响。计算结果表明，锚索振动失稳的范围取决于锚索的动静张力比、锚索的阻尼比和频率比（锚索参数激励频率与锚索1阶模态固有频率的比值）；当频率比为1和2左右时，随着锚索动静张力比的增大和阻尼比的减小，锚索逐渐从稳定状态转变为不稳定状态，且锚索的不稳定区域逐渐增大。

To study the stability of submerged floating tunnel tether, the vortex￣induced vibration equation of tether is set up, which is simplified by Galerkin method. The stability of tether vibration is judged by Lyapunov exponent method. Effects of dynamic and static tension ratio, damping ratio and parametric excitation frequency of tether on its vibration stability are analyzed. The results show that the stability of submerged floating tunnel tether depends on dynamic and static tension ratio, damping ratio of tether and frequency ratio （the ratio of parametric excitation frequency and the first order modal frequency of tether）; when the frequency ratio is around 1 and 2,with the increasing of dynamic and static tension ratio and decreasing of damping ratio, the tether changes gradually from stable state to instable state and the instable region of tether increases gradually.