In order to analyze the vibration stability of submerged floating tunnel tether under two different boundary conditions

the vibration equation of tether was set up. The equation was simplified by Galerkin method. The vibration stability of tether was judged by Lyapunov exponent method. Effects of damping ratio

bending stiffness and span of tether

current velocity and vortex-induced frequency on vibration stability of tether were analyzed and compared under different boundary conditions. It may be concluded that  tether is been gradually from stable state to unstable state as the current velocity increases under two different boundary conditions. The tether tends to be stable as the damping ratio

bending stiffness of tether increases

when the vortex-induced frequency  under two different boundary conditions is close to the tether. It will occur vortex-induced resonance and the tether is easy to be unstable

and the unstable region expands gradually as the current velocity increases under two different boundary conditions

but the unstable region is larger which under the combination sliding boundary.