Nonlinear Vibration Analysis of Submerged Floating Tunnel Tether

Abstract

To study the nonlinear vibration characteristics of submerged floating tunnel tether, the nonlinear vibration partial differential equation of tether is set up, in which the inclination, sag, initial tension force, and length of tether are taken into account. According to the linear vibration mode of tether, the partial differential equation is converted into ordinary differential equations by Galerkin method and the nonlinear vibration equation of tether for the in-plane first four modes and the out-of-plane first four modes are obtained. The results show that the change of inclination results is in the change of sag. The initial configuration of sag is symmetric. Thus, the sag only affects the damping ratio of the in-plane symmetric mode, namely, that of the first and the third mode. The sag has no effect on the second and forth order modes which are antisymmetric modes. Therefore, the sag is only existed in plane and has no effect on the out-of-plane mode. The first and the third in-plane modal damping ratios of tether are in direct proportion to their inclination, whereas in inverse proportion to their sag. The first modal damping ratio of tether (both in-plane and out-of-plane) is in direct proportion to its length, whereas in inverse proportion to its initial tension.