Tension during parametric excitation in submerged vertical taut tethers

Abstract

The construction of a suspension bridge with floating pylons or a submerged floating tunnel requires the installation of a mooring system. The option of taut vertical tethers, similar to those used in tension-leg platforms, has been suggested in preliminary designs. The environmental loading on the tether, mainly due to wind waves and swell, results in a parametrically excited system. Certain loading conditions develop instabilities that translate into large horizontal motion. However, the effects of parametric resonance on the tension values have rarely been investigated. This paper aims to clarify the relation between lateral displacement and tether tension and to quantify the extreme tension values in the event of parametric resonance. The presented analysis is based on a full numerical model of the tether that includes geometric and hydrodynamic nonlinear effects. This model is used to investigate a representative example that illustrates parametric resonance and multiple parametric studies to assess the effects of the excitation frequency, amplitude, initial pretension, tether length and inclination angle on the tether's response. The results reported here provide the basis for a recommendation on designing a tether under parametric resonance regarding the ultimate extreme values and fatigue life.

Coupled Vibration Analysis of Submerged Floating Tunnel System in Wave and Current

“…(1) The first-order vibration frequency of the SFT tube is twice the fundamental frequency of the i # cables (i.e., ω t1 :ω i1 = 2:1), which leads to the principal parametric resonance [18,21];…”

“…(1) The first-order vibration frequency of the SFT tube is twice the fundamental frequency of the i # cables (i.e., ωt1:ωi1 = 2:1), which leads to the principal parametric resonance [18,21]; (2) When the vortex-induced frequency is assumed to be consistent with the cable frequency (i.e., 2πfvi = ωi1), significant VIV of the cables occurs [13,30]. After the determination of ωi1 = 3.493 rad/s in Equation (9), the flow velocity v0 = 1.18 m/s can be further calculated by Equation (4).…”

“…Xiang and Chao [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. Cantero 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.…”

Two elastic supporting models to simulate the submerged floating tunnel and their equivalence on the free/forced vibrations

“…The most common tethered SFT consists of two typical members, that is, tether and tube. With regard to the underwater tether (Wu et al, 2018; Sun et al, 2020), the studies of the cable in air on the parametric/forcing excitation(s) originating from the support motions (Guo et al, 2020) provide modeling suggestions by adding the hydrodynamic forces (Cantero et al, 2017). For the tube, by seeing the tethers as uniform linear elastic foundation, the simple and mature elastic foundation beam (EFB) model (Öz and Pakdemirli, 2006; Mamandi et al, 2012) is widely used to study the vibrations by moving loads (Tariverdilo et al, 2011), synchronous/asynchronous support excitations (Mirzapour et al, 2017; Akbarzadeh et al, 2021), impact and cable breakage (Xiang and Yang, 2017; Xiang et al, , 2018).…”