基于Lyapunov指数的悬浮隧道锚索振动稳定分析

Vibration stability analysis of submerged floating tunnel based on Lyapunov exponent

为分析水下悬浮隧道锚索在均匀流作用下振动的稳定性问题,建立了锚索的振动方程并用伽辽金法对其进行了简化。采用Lyapunov指数法判断了锚索涡激振动的稳定性,同时分析了锚索阻尼比、初张力、均匀流速和涡激频率对锚索振动稳定性的影响。研究结果表明,随着均匀流速的增加,锚索逐渐从稳定状态转变到不稳定状态;锚索振动系统的初张力、阻尼比越大,锚索就越容易趋于稳定状态;当涡激频率与锚索一阶固有频率接近时,会发生涡激共振现象,锚索最容易失稳。

To analyze the vibration stability of submerged floating tunnel under the uniform current, the vibration equation of tether is set up and simplified by Galerkin method, and the vibration stability of tether under the vortex-induced vibration is judged by Lyapunov exponent method. The influence of tether damping ratio, initial tension, uniform flow velocity and frequency of vortex-induced vibration on the vibration stability of tether is studied. It is concluded that the tether is gradually changed from stable state to unstable state as the current velocity increases;the tether tends to be stable as the damping ratio and initial tension of tether increase;when vortex-induced frequency is close to the 1st nature frequency of tether, the vortex-induced resonance would occur and the tether is easy to be unstable.