Nonlinear vibration response of submerged floating tunnel tethers under coupled external current and parametric excitations

This paper first established the equation of vibration control for submerged floating tunnel tethers under coupled parametric and vortex-induced excitations by introducing the Van der Pol wake oscillator model, and by comprehensively considering the bending stiffness and sag effect of the tethers based on Hamilton’s principle. Subsequently, numerical solutions to the equation of vibration control were obtained by using the Galerkin method, Houbolt difference method, and Newton-Raphson iterative method. Finally, the mid-span vibration-induced displacement and characteristics of the vibration frequency of inclined tethers under different frequencies (ω_p) and amplitudes (Z_p) of parametric excitation, and vortex-induced frequencies (ω_v) were systematically studied. The results revealed that the frequency and amplitude of parametric excitation as well as the vortex-induced frequency significantly influenced the system’s vibration response. As these parameters changed, the vibration characteristics of the tether structure gradually transitioned from periodic to quasi-periodic and chaotic states. Specifically, when the frequency of parametric excitation was close to the first natural frequency of the system or twice its value, the tethers exhibited significant parametric resonance that led to a notable increase in the structural amplitude. When the vortex-induced frequency ratio (ω_v /ω₁) was larger than 3, the structure exhibited the characteristics of chaotic vibration. Moreover, the contributions of second- and higher-order modes should not be overlooked when analyzing structural vibration responses under coupled parametric and vortex-induced excitations.