# Coupled Vibration Analysis of Submerged Floating Tunnel System in Wave and Current  
Zhengyang Chen  
College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China;  
[EMAIL_ADDRESS] (Z.C. ); [EMAIL_ADDRESS] (H.L. ); [EMAIL_ADDRESS] (Y.Y.) Yiqiang Xiang  
College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China;  
zjuczy@zju. effect of SFT location depth on the dynamic characteristics. [PERSON] et al. [6] in combination with the SFT conceptual design at Qiandao Lake in China, studied both the static and dynamic responses of the tunnel under environmental loads. The best performing cable configurations were also selected in view of a seismic analysis. [PERSON] [7] used the boundary element method (BEM) and the Morison equation to calculate the wave load acting on the SFT. [PERSON] et al. [8; 9] studied the effects of some basic structure parameters on the dynamic behaviors of the SFT under wave and current via ANSYS software. [PERSON] et al. [10] measured the wave forces acting on the tunnel tube through a model test with scale SFT segments. A good agreement between the experimental results and the values predicted through the Morison equation was observed. [PERSON] et al. [11] evaluated the static and dynamic responses of a SFT under hydrodynamic and seismic loadings. Most of the above research mainly addressed the global performance of the SFT tube based on Morison equations [7; 8; 9; 10; 11]. However, despite that the support stiffness provided by anchor-cables acting on the tube was included in most of these models, the vibration of the cable itself was neglected. Compared with the tunnel tube, oscillation of the SFT cables in fluid flow is more prone to occurring due to the periodic vortex shedding, known as vortex-induced vibration (VIV) [12]. Furthermore, because the top end of the anchor-cable is connected to the tube body, similar to other top-tensioned risers (TTR) in deep water platforms, the cables simultaneously encounter parametric excitations due to the time-varying tension which results from the motions of SFT tube under the environmental loads (such as regular waves) [13; 14; 15]. Hence, the local dynamic behavior of the cables is always a key problem in the design stage. There is little research on SFT cable vibration undergoing parametric excitations and VIV. [PERSON] and [PERSON] [16] used the Monte Carlo method to analyze the parametric vibration response of a simplified coupled tether-tube system subjected to random excitation. [PERSON] et al. [17; 18] developed an analytical model for analyzing marine cables of SFT under combined fluid loads and random seaquake excitations. [PERSON] and [PERSON] [19] once performed a vibration analysis of the SFT system to evaluate the VIV of the cables, but the wave force on the tube body was not taken into account. [PERSON] et al. [20; 21] analyzed the mooring cables' stabilities under parametric excitations. They also studied the effects of parametric resonance on the tension forces of the vertical tethers in ABAQUS. Meanwhile, more research has been directed toward the dynamics of TTR under combined vortex and parametric excitations by means of FEM, semi-empirical models [13; 14] and experimental investigations [15]. In these existing models for single marine risers, the upper floating platform has usually been regarded as a rigid body rather than a deformable one, and is represented as a pre-defined harmonic excitation. This means that these vortex-induced and parametric vibration prediction methods are not entirely applicable to the SFT cables. From the above literature review, we can find that the tube or anchor-cables have usually been studied separately. While the tunnel is the main research object, the tunnel and cables are treated separately as a beam and linear springs, so the cable vibration is not excited. The other model focused on the motion of one single cable, regarding the tube as a mass block, which means the bending vibration of the tunnel is simplified.