Cable Response Research Articles

Experimental study on vortex-induced vibrations of double-hanger cable: Upstream wake flow induces downstream vibrations

This study is inspired by an experimental observation for vortex-induced vibrations (VIVs) of a double-hanger cable system, in which a smaller vibration of the downwind hanger cable is re-excited over a narrow range of wind speeds beyond the “lock-in” range. This phenomenon is known as the wake vortex-induced vibrations (WVIVs), where the upstream wake flow induces downstream vibrations. To further investigate the characteristics and reasons for WVIVs, a refined wind tunnel test of double-hanger cable was conducted to consider the influence of aerodynamic interaction. The double-hanger cable was modeled by the tandem-arranged spring-mounted cylinders vibrating in two dimensions. The vibration responses of hanger cables were obtained under various wind speeds to reproduce the lock-in phenomenon. In addition, the vibration trajectory, phase relationship, damping ratio, inter-cable correlation, and the wind pressure on the surface of cables were analyzed. Finally, the Stockbridge dampers were designed to suppress the vibrations. The results show that under the aerodynamic interaction of the cables, the onset wind speed of VIVs in the double cables increases, and the downstream cable WVIVs closely follow the VIVs. During the WVIV phase, the downstream cable behavior is characterized by increased negative aerodynamic damping and an inverse displacement correlation between the cables. The phase relationships between the cables are time-varying due to the aerodynamic interaction. The first proper orthogonal decomposition mode of wind pressure dominates the cross-wind of motions and is crucial in vibrations. Stockbridge dampers can effectively reduce the amplitude of VIVs and eliminate WVIVs in cables.

Cable coupling response in metal cavity under X-ray irradiation

Cable coupling response in metal cavity under X-ray irradiation

Cyclic response and stability of shape memory alloy cables considering training, displacement history, and prestrain effects

Superelastic shape memory alloy (SMA) cables have been considered in the development of various seismic protection technologies. The cyclic nature of seismic loads necessitates a comprehensive understanding of the mechanical behavior of SMA cables under repeated loading conditions. As SMAs undergo repeated phase transformation cycles, alterations in their properties occur due to defects generated and modified during the transformation. When utilizing superelasticity, this response can be stabilized after numerous transformation cycles. In various applications, components made of SMAs undergo a stabilization process referred to as training to enhance the predictability of the alloy’s response. Despite the widespread acceptance of training cycles to achieve stable cyclic response, a well-defined protocol is lacking. This study investigates the effects of various factors, including training strain amplitude, repeated loading, low-cycle fatigue loading, loading at high strain amplitudes, displacement loading history, and prestrain on the cyclic response of a large-diameter SMA cable. A total of 14 SMA cable specimens are tested under various tensile loading conditions. The experimental results, including stress-strain curves and various response parameters such as peak stress, residual strains, energy dissipation capacity, and equivalent viscous damping are examined in detail. The results indicate that training SMA cables at a strain amplitude near the end of phase transformation plateau leads to a highly stable cyclic response. However, it is worth noting that, in comparison to untrained cables, training induces a softening effect in the cable response.

Short-term extreme response estimation methodology for marine umbilical cables with two configuration types

This study investigates the critical engineering problem of the short-term extreme responses of marine umbilical cables, which are essential components in offshore oil and gas operations. Umbilical cables play a pivotal role in connecting subsea systems to surface platforms, necessitating a safe design to withstand external loads. This study focused on two primary umbilical cable configuration types: deep-water catenary and shallow-water lazy wave. For each configuration type, 100 3-h dynamic numerical simulations were performed, with maximum values fitted by using the Gumbel distribution, and the most probable maximum (MPM) values were set as benchmark values. The average conditional exceedance rate (ACER) method and uncertainty-incorporated ACER method were applied to study the short-term extreme values of umbilical cable responses based on limited sample data. The predicted results have been compared with the MPM values, and the accuracy and uncertainty of different efficient extreme-value analysis methods are discussed. This study provides a comprehensive methodological framework for the reliability analysis and safety design of umbilical cables in marine engineering.

Spectral Analysis of a Sagged Cable with an Optimal Viscous Inertial Mass Damper under Random Wind in a Generalized State-Space Formulation

In this study, a spectral analysis method is proposed for a sagged cable with an optimal viscous inertial mass damper (VIMD) under random wind loads based on a generalized state-space formulation. The frequency response functions of the cable responses were evaluated for the wind force vector using complex modes orthogonal to the system matrices, from which the power spectral densities of the cable responses were readily obtained for the spectral matrix of the wind force. The accuracy and efficiency of the proposed method were verified by comparing the root mean square responses with those obtained from the time-domain and covariance analyses. The performance of two VIMDs optimized by the fixed-point method and the maximum damping ratio method was investigated for various cases of cable sag and wind properties. Serviceability failure probability analysis was also conducted using the first-passage problem. The results show that the proposed spectral method is computationally more efficient than the other two analysis methods. The VIMDs optimized for the first original cable mode were found to be highly effective in reducing cable vibration and the probability of serviceability failure.

Integrated numerical investigation of a 15 MW semi-submersible wind turbine at moderate water depth

Numerical simulations of dynamic responses of 15 MW offshore floating wind turbine are performed by an integrated FAST-OrcaFlex coupling model. An integrated model is established for an IEA 15 MW reference wind turbine (RWT) mounted over a semi-submersible floating platform, where the mooring line system and dynamic cable are designed at a moderate water depth h = 50m. The dynamic responses of 15 MW FOWT, mooring line system and dynamic cable are discussed, and the characteristics of load, displacement, mooring tension and bending curvature of dynamic cable at different IEC design load cases are investigated by the integrated time-domain simulations. The results indicate that the mean response of 15 MW FOWT is found to be mainly depended by the wind load, while the standard deviation of response is mainly influenced by the wave load. The mooring line system remains within the safe design range during the extreme environmental conditions. Moreover, the dynamic response of dynamic cable is influenced by the combined effects of the floating platform and ocean environmental factors. Large curvatures are observed in the buoyancy and boundary-layer sections, and high tensions are observed at the hang-off point, decline section and anchor point.

Numerical Analysis of Cable SGEMP Responses in Multiwire Bundles

Numerical Analysis of Cable SGEMP Responses in Multiwire Bundles

Design and Analysis of a Buoy-Based Cable Seafloor Observatory System Response under Extreme Weather Conditions

In order to address the requirements of scientific multidisciplinary observation in diverse small-scale regions, we have introduced the Buoy-based Cable Seafloor Observatory System (BCSOS). This system offers a distinct advantage in contexts where the use of shorter cables is feasible, contrasting with the lengthy cables typically necessary for conventional observatories. The BCSOS consists of three primary components: the Real-Time Electric Communication (RTEC) Buoy, the Power Information Transmission System (PITS), and the Seafloor Observation Subsystem (SOS). The RTEC Buoy is equipped with instruments for measuring sea surface parameters and serves as a data and power hub. The PITS, comprising a robust EM cable, connects the buoy to the SOS, which houses instruments for seafloor observations. The system is designed for a maximum water depth of 100 m and has an expected lifespan of about 5 years. The BCSOS prototypes were deployed at the Huangqi Peninsula, Fujian Province, and successfully documented the process during Typhoon Doksuri (international code 2305) at the end of July 2023. The recorded data from the BCSOS revealed a significant increase in wave height and period as the storm approached the Huangqi Peninsula. Additionally, the RTEC buoy exhibited a notable response to the large waves. The data analysis revealed a distinct pattern between the buoy response and the direction of wave propagation across various sea conditions, that the buoy’s angular movement in pitch and roll directions follows a regular elliptical distribution corresponding to different wave propagation directions. Upon thorough evaluation, future enhancements to the system are slated to concentrate on refining its design, with a particular emphasis on bolstering stability and enhancing corrosion resistance. These improvements are aimed at cementing the system’s long-term viability and performance within the challenging marine environment.

Dynamic Response Analysis of Moving Loads over Tension Cables of Connected Tower Cable-Stayed Bridge

Due to its strong crossing ability, cable-stayed bridges have become the mainstream bridge type for large and medium spans. The connected tower cable-stayed bridge is different from traditional single span cable-stayed bridges, integrating the characteristics of split frame structure and connected tower design, and has better structural mechanical properties. However, the complex cable layout, multi tower structure, and segmented bridge deck of the cable-stayed bridge with connected towers result in essential differences in its mechanical behavior compared to traditional bridges. Therefore, studying the dynamic response of cable-stayed bridge cables when vehicle loads pass through the bridge is of great practical significance. This article comprehensively considers two factors: vehicle weight and vehicle speed, and introduces the parameter of dynamic amplification factor. The numerical simulation method is used to analyze the dynamic response of the cable when a vehicle load passes through a cable-stayed bridge with a connected tower. In order to provide key data support and important references for the construction and operation monitoring of cable-stayed bridges with connected towers.

Nonlinear motion modeling and analysis of underwater cables under complex loads based on global nodal position finite element method in Hamiltonian formulation

The nonlinear dynamic response of underwater cable is essential for underwater equipment system. This paper presents an effective global nodal position finite element method in Hamiltonian formulation to investigate the nonlinear motion of underwater cable under complex loads. The method fully considers the axial, bending, torsional and shear deformation of underwater cable. The non-linear Green-Lagrange strain-displacement relationship is applied to obtain the strain energy. Furthermore, the fourth-order circular cross-section quadrature is introduced to integrate the volume of underwater cable element after deformation. The dynamic governing equations in Hamiltonian formulation are derived and converted into the corresponding canonical equations, which are calculated by the symplectic difference algorithm. Then an initial curved pendulum system, a 180° turn towed underwater cable system and the spiral turning motion of ROV are designed to verify the presented method. The results show that compared with the existing Hamiltonian global nodal position finite element method which ignores torsional and shear deformation, the proposed method is more accurate in describing the nonlinear motion of the underwater cable with axial, bending, torsional and shear deformation.

Research on cable dynamic response of a catenary anchor leg mooring system based on ANCF

This paper presents a dynamic analysis model for a catenary anchor leg mooring (CALM) system based on the absolute nodal coordinate formulation (ANCF) method, combined with continuum mechanics and finite element theory. This model uses absolute slope coordinates instead of traditional angle coordinates to better describe the large deformation and large displacement of the cables. The paper derives the element mass matrix, generalized stiffness matrix, and the element external load matrix, including the Morison force transformed into the ANCF framework, based on the virtual work principle. The accuracy and reliability of the ANCF program are validated using static and dynamic beam models, as well as submerged tether models. Furthermore, a comparative analysis of the ANCF mooring cable model with OpenFAST and MoorDyn accentuates the program's practical value in real engineering applications. Finally, we systematically analyzed the dynamic characteristics of a CALM single-point mooring system, revealing that the mooring forces in the cables significantly influence the high-frequency motion of the buoy. Additionally, the reduction in the length of the mooring cables, to an appropriate extent, enhances the stability of the system, which further attests to the effectiveness and practicality of the ANCF model that has been developed.

Lightning current Risetime influence on inductive coupling effect of secondary shield cable in substation

Secondary cables are susceptible to lightning surge currents when substation is struck by lightning. Little work has been made to the effects of surge currents in substation secondary cables, particularly the effects of surge current rise time. Six types of simulated lightning surge currents with different rise times, ranging from 5.7 μs to 25.4 μs, were injected into the substation grounding grid, and the inductive voltage from core wire to ground and the shield current in the closed loop of the buried secondary cable were measured simultaneously. The inductive coupling characteristics and the effect of rise time on shielding factor (SF) of buried secondary cables were investigated using time-frequency domain method. The results indicate that the surge current with shorter rise time will induce higher core-wire voltage and higher the shield current on the secondary cable. Double-end grounding of the shielding layer can significantly reduce the cable coupling response, especially reduce the high-frequency component of the inductive voltage at 10 to 100 kHz with steeper surge currents. The SF of secondary cable increases exponentially from 1.91 dB to 8.15 dB as the rise time of the lightning surge current decreases.

Aerodynamic performance and wind-induced response of carbon fiber-reinforced polymer (CFRP) cables

To study the aerodynamic performance and wind-induced response of carbon fiber-reinforced polymer (CFRP) cables, CFRP cable was designed by replacing a steel cable in a tied arch bridge based on stiffness, strength and area equivalent criteria, respectively. The aerodynamic performance and wind-induced response of CFRP cable and steel cable were studied and compared by computational fluid dynamics (CFD) model. Based on the computational results, optimal cable replacement criterion was proposed for CFRP cable to replace steel cable. In addition, surface modification was conducted by engrooving vertical symmetric (VS), vertical asymmetric (VA) and helical symmetric (HS) V-shaped grooves to improve the aerodynamic performance and wind-induced response of CFRP cable. Results showed that CFRP cables exhibited inferior aerodynamic performance and wind-induced response in most cases. However, CFRP cable based on stiffness equivalent criterion exhibited better aerodynamic performance and wind-induced vibration properties compared to the other two cable replacement criteria, thus is regarded as the optimal substitute for steel cable. In addition, HS grooves generated symmetric disturbances and caused approximately equivalent boundary layer separation delays uniformly and continuously along the cable length, thus exhibiting better effect in decreasing the reverse flow region, the maximum negative flow velocity, the vortex shedding frequency and the wind-induced vibration amplitude of CFRP cable. Hence, the stiffness equivalent criterion combined with surface modification with HS V-shaped grooves was proposed to replace steel cable with CFRP cable. This study can provide insights into the aerodynamic performance and wind-induced response of CFRP cable and instructions for cable replacement practice.

On the Natural Keulegan–Carpenter Number for Subsea Industrial Modulus Installation

Abstract The behavior of subsea equipment has been widely studied by companies to minimize risks during subsea installation, which brings huge costs to the operation. The prediction of equipment motions typically is accomplished by utilizing either commercial software or recommended practices from Classification Societies to comply with the minimum requirements for launching operations. This article analyzes subsea installation in time and frequency domains using experimental, numerical, and analytical approaches. Experiments have been carried out at Instituto de Pesquisas Tecnológicas (IPT) to investigate the dependency of drag and added mass coefficients on Keulegan–Carpenter (KC) number and at Laboratory of Waves and Currents (LOC-COPPE/UFRJ) to study equipment and cable responses on the installation. A numerical model is made in orcaflex® for determining the transmissibility of displacement and force in function of frequency ratio, and the time series of manifold responses. Linearized models from DNV (DNV-GL, 2017, “Recommended Practice (DNVGL-RP-N103) – Modelling and Analysis of Marine Operations.”) and the so-called natural KC (proposed in the present article) are taken in the investigation and compared to previous methodologies. The natural KC approach arises as an innovative way of investigating subsea equipment as the literature only provides parametric analysis considering an arbitrary KC value (i.e., Pestana et al., 2021, “Subsea Manifold Installation: Operational Windows Estimation Based on Hydrodynamic Model Testing,” Ocean. Eng., 219, p. 108364). The analyses notice a good agreement among experiments, orcaflex® model, and natural KC model, whereas the curves found by the DNV method usually overpredict the response of subsea equipment, especially around resonance region.

Simulation analysis of flow field and vortex-induced vibration characteristics of submarine cable under single/parallel-laying mode

Due to the long-term erosion of current, the submarine cable buried on the seabed surface easily causes fatigue damage to the lead sheath, which gradually progresses with time. In this paper, a two-dimensional spring-damping vortex vibration model is established considering the effect of transverse flow and in-line flow. The vortex-induced vibration response of suspended submarine cables under the influence of different parameters is simulated by using the slice method based on nested grids. The simulation model is used to simulate the flow field characteristics and vortex-induced vibration response of submarine cables under single laying and parallel laying conditions. The fluid-solid coupling mechanism between fluid and structure and the interaction law of parallel laying submarine cables are analyzed. Our study overcame the difficulty in testing the vortex-induced vibration of submarine cables and provided a viable method and empirical support for investigating the vortex-induced vibration properties of submarine cables and fatigue analysis.

Analysis on the low-frequency electromagnetic pulse coupling to horizontal electrically short lines

In this study, we investigated the coupling features of the nuclear electromagnetic pulse (NEMP) on overhead cables in the middle-and-far regions, different from the transmission line model commonly used for field-line coupling in high-frequency cases, using a simpler lumped approximation to solve the electrically small size model in low-frequency cases. To verify its effectiveness, a simulation model with the same conditions was set up using the software of Computer Simulation Technology (CST), and cable coupling experiments were performed in a laboratory environment using a bounded-wave electromagnetic pulse simulator. The calculated results of the lumped approximation circuit were compared with the CST simulation and measured results, and the agreement was good. The results also shows that the load exhibits a differential response in the case of the low impedance and it is consistent with the excitation signal in the case of the high impedance. Finally, some more experiments were constructed to analyzed the effect of different cable parameters on the cable load response through experiments, and the experimental results are also in general agreement with the theoretical analysis, in which the induced signal of the low-impedance load is mainly determined by the magnetic field in the direction normal to the cable and the ground loop and the induced signal of the high-impedance load is mainly determined by the electric field in the direction of the height of the cable erection.

A hybrid self-centering seismic damper: Finite element modeling and parametric analysis

This study presents a finite element model for a hybrid self-centering damper considering the rate and temperature effects and explores the effects of different design parameters on the damper response. The damper, called as superelastic friction damper (SFD), consists of superelastic shape memory alloy (SMA) cables and a frictional energy dissipation mechanism. The experimental response of the SMA cables, frictional unit and overall damper at different loading frequencies and temperature are used to develop numerical model of the damper. Once a validated numerical model is obtained, parametric studies are carried out to evaluate force-displacement response of the damper when the design parameters are altered. The effects of damper design parameters on the equivalent stiffness, dissipated energy, equivalent viscous damping and self-centering capabilities of the damper are analyzed. Based on the findings, the recommendations for the design of the damper are presented.

Numerical modeling and fatigue analysis of the dynamic response of main pump cable in nuclear power plant

Abstract The structural temperature rise and thermal stress caused by operation current and ambient temperature are some of the main factors affecting cable fatigue life. Combined with the operating and environmental conditions of the main cooling pump of the nuclear power plant, the thermal-structural coupling field numerical modeling and fatigue analysis of the 6kV single-core and three-core cable of the main pump is carried out. Based on obtaining the steady-state operating current, the motor start-up transient current, and the circulating ambient temperature, the thermal-structural coupling field numerical model of the main pump cable is established using the load transfer method to obtain the thermal and stress field distribution of the internal structural layer. The load history of one cycle is extracted for the fatigue numerical simulation of the main pump cable. The stress time history of the cable structure layer was constructed by the stress calculation results and the load time history of a single period, and the fatigue life of the main pump cable was obtained based on the S-N curve of the main insulation material and the Miner’s linear cumulative damage theory. The simulation results show that the force acting on the main pump cable by the operating current and ambient temperature is an approximately symmetric cyclic load of constant amplitude. The life cycle of the cable can reach 2.235*e4 times, and the overall life of the cable is about 63.97 years. This study can provide theoretical guidance for the safety and reliability design and state operation and maintenance of the main pump cable of the nuclear power plant.

Robustness Evaluation of Negative Stiffness Damper for Cable Vibration Mitigation Based on Interval Model with Experimental Validation

The negative stiffness damper (NSD) has emerged as a promising passive vibration control device for cable structures due to its simplicity and effectiveness. However, uncertainties stemming from both internal and external environmental factors can potentially compromise the NSD’s performance in real‐world applications, posing risks to cable safety. In response, this paper conducts a robustness evaluation on an integrated cable‐NSD system, taking into account various potential uncertainties. Specifically, the uncertain parameters are described by interval variables. Consequently, an interval model is constructed to delineate the boundaries of cable dynamic responses when subjected to these uncertainties. The model’s accuracy is validated against experimental results. Subsequent simulations involve assessing interval responses for both single‐ and multimode cable vibrations under varying uncertainties. Finally, the NSD’s robustness concerning cable vibration control is evaluated using the model, which incorporates the first‐passage theory. This analysis delves into the relationships among confidence levels, performance measures, and the variation range of uncertainties. The results indicate that for single‐mode vibration control, there is a 90% confidence level that the damping ratio reduction remains within 10%. As for multimode vibration control, a 90% confidence level is established that the amplification falls within 17%.

Calculation of Cable SGEMP Response for PCB Trace Based on Finite Element Method

Calculation of Cable SGEMP Response for PCB Trace Based on Finite Element Method