Cable Vibration Research Articles

Free vibrations of shallow inextensible cables: a perturbation approach

Free vibrations of shallow inextensible cables: a perturbation approach

An Experimental Study on Vortex-Induced Vibration Suppression of a Long Flexible Catenary Cable by Using Vibration Dampers

In this paper, an experimental study is conducted to investigate the effectiveness of vibration dampers in suppressing vortex-induced vibration in a long, flexible catenary cable with a low mass ratio. The dampers, consisting of two small, symmetric, lightweight pipes clamped to the cable, are sparsely deployed along the cable to shape the vibration characteristics. The experimental results demonstrate that dampers significantly reduce the vibration amplitude by up to 60% and axial tension by up to 61% at high flow velocities, effectively suppressing the cable vibration in perpendicular flow. In addition, it is observed that the in-line and cross-flow vibration frequencies are approximately equal when the dampers are applied. This behavior contrasts with the conventional undamped catenary cable, where the in-line vibration frequencies are double those of the cross-flow frequencies.

Intelligent vibration control of tensile cable based on deep reinforcement learning

Vibration of tensile cables commonly occurs in the engineering structures such as cable-stayed bridges, which may have negative effect on the driving comfort and safety, and further lead to the fatigue problems of the structure. This paper proposes a semi-active control strategy based on deep reinforcement learning and magneto-rheological (MR) damper, for the vibration control of tensile cables, and the corresponding algorithm have been developed. Through the interaction with the cable-damper system, the intelligent agent can evaluate every possible control parameter and achieve an effective control policy. Then, according to the real-time vibration state, the agent would determine an action current for the MR damper and thus change the damping coefficient of the damper, further make influences on the vibrating cable. Basically, the proposed strategy realizes the model-free semi-active control of cable vibrations. To validate the effectiveness of the proposed semi-active control strategy, a scale model test has been conducted, where the test cases of passive and semi-active control strategies are carried out and compared. Results show that, the semi-active control shows a prior performance in vibration reduction compared to the passive control strategy, with regard to the vibration profile, the vibration energy, as well as the energy dissipation of MR damper.

Field observation and cause investigation of low-frequency cable vibrations in a cable-stayed bridge

Considerable levels of stay cable vibration in cable-supported bridges pose significant challenges for safety, operation, and maintenance. An accurate understanding of the specific causes and types of vibration is essential for effectively addressing this problem with an optimal design for mitigation measures. This study aims to investigate the cause of an extraordinary low-frequency vibration that occurred at a stay cable by employing comprehensive methodologies. The modal properties and vibrational characteristics of cable vibrations were first obtained through finite element modeling, operational modal analysis, and vision-based displacement measurements. Subsequently, the primary cause of low-frequency vibrations was investigated using field observations and wind tunnel tests. Field-monitoring data revealed that stay cables were excited by small deck vibrations. The critical wind speeds at which deck vibrations occurred in a wind tunnel experiment were aligned with the ranges of wind speeds that produce low-frequency cable vibrations, which confirmed that these two phenomena are manifested under similar wind conditions. A calculated support excitation amplitude, determined via the use of an empirical equation, exhibited consistency with vision-based measured displacement obtained in field experiments. These findings underscore the potential risk of support excitation between minor deck vibrations and cables, which provides valuable insights that could mitigate cable vibrations.

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.

Experimental recurrence of an unreported fire risk of power cable: Discharge of bracket cable metallic grounding under coupled vibration conditions

In environments like bridges and tunnels, power cables are laid on metal brackets (hereinafter referred to as bracket cables). If the aluminum sheath and metal bracket form a metallic grounding fault, the air gap near the contact point may bear an intermittent discharge under the cable vibration, which is a potential source of cable fires. However, current research on cable grounding systems does not focus on analyzing the physical metallic grounding process. Discharge from coupled vibrations has been overlooked. This study accomplished the experimental recurrence of discharge at the metallic grounding point of cables under coupled vibration. According to the experimental observations, intermittent electric sparks and AC arc occur with the contact and separation of the aluminum sheath and the metal bracket due to vibrations. Under coupled vibration conditions, metallic grounding faults in cables pose a risk of causing cable fires.

Experimental study of vortex-induced vibration of stay cables installed with two types of perforated shroud light devices

To address both illumination issues and the common vortex-induced vibration (VIV) of bridge cables, a perforated shroud light device is proposed. The effect of the different porosities (20%, 35%, 42%, and 55%) on VIV of the rigid segmented shroud cable models is studied first by wind tunnel tests. It reveals that shrouds with porosities of 20% and 35% could reduce the VIV amplitude of the smooth cables by 26% and 46%, respectively. However, shrouds with porosities of 42% and 55% tend to increase the complexity and risk associated with VIV. Vibration measurements on flexible should cable with 20% porosity were conducted for both vertical and inclined models with an inclination of 35° and yaw angles of 0°, 30° and 60°. Shrouds with a porosity of 20% exhibit similar effects on vertical flexible cables as on horizontal rigid cables, in both cases mitigating VIV. The impact on the inclined flexible cables depends on the yaw angle. At the yaw angle of 0°, the shroud effectively mitigates VIV in flexible cables. However, at yaw angles of 30° and 60°, the same porosity level shroud exacerbates the risk of VIV in the inclined flexible cable. This may be due to the enhanced wind velocity along the cable axial direction and decreased penetrating flow rate through the shroud as the wind yaw angle increases. Overall, it was found that a shroud with a porosity of 20%–35% performed the best and was recommended for applications on cables with no inclination and inclined cable at yaw angle β = 0°.

Investigation into fatigue failure of cable brackets and vibration suppression methods

The cable bracket is one of the most important components of high-speed EMUs, as it supports the cables of sensors. The fatigue failure of the bracket can severely affect the operation of the vehicle. In this study, the dynamic response of the cable bracket, including dynamic stress and acceleration, is obtained through field tests. The results show that the modal vibration of the bracket excited by high-frequency excitation in the wheel–rail system is an important cause of fatigue failure of the bracket. Rail welded joints in the track and polygonal wear of the wheelset further exacerbate the vibration and of the bracket. A model of the virtual vibration table is proposed to simulate the actual excitation experienced by the bracket. The effects of the cantilever beam length, steel plate thickness, and pre-tightening torque of the bolts on the dynamic stress of the bracket are studied using the virtual vibration table. Several vibration suppression methods are proposed. The results indicate that the dynamic stress of the bracket caused by the rail welded joints can be effectively reduced through the adjustment of the pre-tightening torque of the bolts or the appropriate reduction of the cantilever beam length. The findings of this study can serve as a reference for suppressing vibration and preventing fatigue failure of the bracket.

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.

Numerical simulations on cables attached with different shapes of lights and its mitigations by using perforated shrouds

To reduce the cable vibration caused by rectangular lights, the light shape is modified to be ellipsoidal and circular sections, together with the use of a perforated shroud. Numerical simulations on six types of cable-light models were conducted using computational fluid dynamics. The mean drag coefficient CD, mean and mean lift coefficient CL, mean of the ellipsoidal lights, circle lights, and perforated shroud cable are reduced compared to the rectangular light. CD, mean can be reduced by a maximum of 50%; CL, mean can be reduced by a maximum of 43%. The maximum fluctuating drag and lift coefficient are also significantly reduced. This indicates that the perforated shrouds might be useful to mitigate the vortex-induced vibration. The ellipsoidal and circular lights are significantly better than rectangular lights in terms of galloping critical wind speed. Furthermore, the perforated shroud is very beneficial for suppressing galloping vibration. The variation of Strouhal number St with the wind attack angle for the shroud rectangular light cable model is relatively smooth, all around 0.1. The wake vortices of rectangular light, ellipsoidal light, and circular light are shed alternately in a typical 2S pattern. However, the alternately shedding vortex of the shroud cable was interrupted by the flow of air through the holes. When the wind attack angle exceeds the most dangerous wind attack angle, the incoming stream cannot be reattached after separation, and the force on the cable is greatly reduced, resulting in a sudden drop in the average lift coefficient. Wind pressure in the gap between the shroud and the cable is negative. The fluctuating wind pressure coefficients on the shrouded cables are significantly lower than those of rectangular lights because of the interference effect of the outer perforated shrouds. In total, the perforated shroud is the best to reduce the galloping caused by the rectangular light.

Vibration Suppression of Two Adjacent Cables Using an Interconnected Tuned Mass Damper/Nonlinear Energy Sink

Due to their high flexibility, low damping, and small mass, stay cables are prone to large-amplitude vibrations. Various mechanical measures, typically installed near the cable anchorage to the deck, have been developed to suppress cable vibration. These dampers, however, may not be effective for ultralong cables since the damper is close to the cable anchorage, the cable node. In this paper, a tuned mass damper (TMD)/nonlinear energy sink (NES) are considered for installation between two adjacent stay cables for vibration mitigation. Firstly, the static equilibrium equation of the stay cable–damper system is established, and the influence of the self-weight of the damper on cable shape is investigated. The governing equations describing the motion of the two adjacent cables with a damper are then established using the Hamilton principle, which are then solved by the method of separation of variables. For cases of swept-sine excitation and harmonic excitation, the optimal designs of TMD and NES are achieved with the purpose of suppressing the first- and third-mode-dominated vibrations, respectively. Both optimal TMD and NES may substantially suppress cable vibrations, with each having advantages under certain situations. Finally, the dynamic response characteristics of two adjacent cables with an optimal damper are analyzed. Interesting dynamic behaviors, such as energy input suppression, phase shift, cable frequency shift, and phase diagram boundary rotation, are identified, and their mechanisms are explained.

Parameter Tuning and Positioning Strategy of VD and TMD Joint Control System for Multi-Modal Vibration of Stay Cables

Stay cables are becoming slender and their fundamental frequencies are becoming lower with the span of bridges increasing, thus leading to the occurrence of multi-modal vibration under various excitations. As a simple and effective strategy for cable vibration mitigation, the external damper is widely used in practice. However, one damper normally can target only fewer modes and poses limited effects on the control of multi-modal vibration. This paper proposed the use of a joint control system combining a viscous damper and a tuned mass damper for mitigating the multi-modal vibration of stay cables, followed by the optimization methodology of tuning and positioning. The control performance of the joint system was evaluated by numerical simulations. The feasibility of the joint control system was validated by analyzing the results of the comparative study, therefore providing a possible solution to multi-modal and high-modal vibration of stay cables.

In-plane free vibration of a two-cable network with multiple flexible cross-ties considering the effects of dynamic axial forces of the cables

Equipping cross-ties on the cables of cable-stayed bridges to form a cable network is regarded as an effective measure to suppress large cable vibrations and has been realized in practical engineering. However, most of the existing studies on the suspended cable (small sag) network have ignored the contributions of dynamic axial forces to transverse forces of the cables. More importantly, the dimension of the characteristic matrix is relatively large. Therefore, the current study introduces the transfer matrix method (TMM) to solve the in-plane free vibration problem of a two-cable network with dynamic axial forces of the cables considered simultaneously. Compared with the methodology utilized by the previous studies, the dimension of the resulting characteristic matrix is smaller and is independent of the number of cross-ties. Three cases, i.e., a two-cable network with two cross-ties, with three cross-ties and with four cross-ties, are explored in detail. Their frequencies and mode shapes are compared with those obtained by finite element model (FEM) to demonstrate the validity of the results in this paper. Meanwhile, the effects of dynamic axial forces on the first two frequencies and mode shapes are analyzed. The results show that the contributions of dynamic axial forces should be taken into account in transverse forces when calculating the first two frequencies of the cable network with flexible cross-ties.

A study on vortex-induced vibration of a long flexible catenary cable in perpendicular flow

In this paper, a numerical model based on Euler-Bernoulli beam theory and a single van der Pol wake oscillator model is proposed to study the vortex-induced vibration of a long flexible catenary cable with a low mass ratio. The wake model uses only one oscillator to describe the in-line and cross-flow vibration with consideration of their nonlinear coupling. An experiment on a flexible cable model in perpendicular flow is carried out to validate the proposed numerical model. Numerical results and experimental measurements are compared on the vortex-induced vibration responses including the maximum amplitude, axial tension, and vibration frequency. A sensitivity analysis of the parameters used in the numerical model has been carried out. Numerical simulations by the proposed numerical model with properly selected parameters have demonstrated that the vibration frequency and the axial tension can be well predicted, and the variation of the vibration amplitudes can also be properly captured. The lock-in phenomena and the axial tension variation of the long flexible catenary cable in perpendicular flow have been carefully studied both numerically and experimentally.

Cross-ties with linear hysteretic damping for cable vibration mitigation: Theoretical analysis and full-scale experiment

This study investigates cross-ties with linear hysteretic damping (HDCs) for vibration mitigation of stay cables through theoretical analysis and full-scale experiments. The formed cable networks are modeled by considering cables as taut strings and the HDCs as mass-less elements of complex stiffness. Frequency equation of the system is formulated analytically and is solved numerically. Then, the influence of HDCs on system dynamics is discussed for typical cable networks and considering HDCs realized by a rigid tie in series with high damping rubber. The results indicate that the HDCs can realize high damping for multiple modes because of the frequency independency of hysteretic damping and no restriction on the installation location. Increasing the loss factor of the cross-tie is significant for improving system damping, but less effective for system frequency modification. Extending HDCs to the ground and using multiple HDCs are effective in further enhancing multi-mode frequency and damping of the system. Furthermore, full-scale experimental validations and investigations are conducted based on three cables of approximately 40 m. Experimental results have validated the effectiveness of HDC in enhancing system damping. This study demonstrates that the easily implementable HDCs have excellent performance in vibration mitigation of multi-mode cable vibrations.

PMFSE: a video phase-based micro-vibration measurement algorithm for bridge cables in complex background

The cable serves as the primary structural component in cable-stayed bridges, suspension bridges, and other cable-supported bridge designs. Accurate measurement of cable tension holds paramount importance for ensuring the overall safety and stability of bridge structures. Cable tension can be inferred from the vibration frequency, making precise measurement of cable vibration frequency of utmost practical significance. Presently, video-based methodologies, such as phase-based vibration extraction, present notable advantages in terms of speed, efficiency, and non-contact capabilities over conventional acceleration sensor approaches. However, these methods face challenges in accurately discerning the micro-vibration of cables in complex background interference. To address this problem, a phase magnification-based feature signal extraction (PMFSE) algorithm is proposed, which is suitable for detecting small vibration in complex background. The overall idea is to combine the small vibration enhancement method in spatial domain with the signal separation method in time domain. Specifically, in the spatial domain, edge phase information is amplified through phase amplitude weighting and phase enhancement techniques to mitigate non-edge noise. In time domain, cable signals are extracted based on distinguishing features between the cable signal and noise signal. The efficacy of PMFSE is evaluated in various outdoor experiments. Compared with the state-of-the-art methods, PMFSE exhibits substantial improvements on the cable micro-vibration frequency measurement in complex background.

Optimal design of transverse dampers incorporating inherent stiffness effects for stay cable vibration control: A case study with wire rope dampers

This paper aims to develop an optimal design method for dampers incorporating inherent stiffness effects for cable vibration control. An explicit solution incorporating the inherent stiffness effects of dampers was proposed to predict the modal damping ratio of a cable-damper system, including both low-mode and high-mode vibrations. The explicit solution is in good agreement with the numerical results. An optimization method was established to quickly determine the optimal design parameters of the damper, using the modal damping ratio of the cable as the optimization criterion. Wire rope dampers, proven promising in cable vibration control, were taken as a case study. Extensive cyclic loading tests were conducted in this study to investigate the influences of design (geometric) parameters on the damping performance of wire rope dampers. Experimental results indicated that the loop mean diameter and rope diameter have nonlinear effects on the damping performance, while loop number exhibits a linear effect. The response surface formulas were developed by using experimental data to describe the geometric influences of wire rope dampers. The developed design method was used to optimize the wire rope damper installed on the stay cable of the Sutong Yangtze River Bridge. A dual damper arrangement was found to be significantly superior to the existing damper arrangement, not only increasing the modal damping ratio but also reducing the damper cost. The optimization design was verified by the harmonic response analysis and sinusoidal load excitation analysis results.

Effect of Stratified Flow on the Vibration of Anchor Cables in a Submerged Floating Tunnel

This study investigates the vertical-type submerged floating tunnel with anchor cables. Based on the characteristics of the anchor cables, the anchor cables are simplified as a nonlinear beam model with hinged ends. Disregarding the axial displacement of the tunnel body, the loads will cause displacements in the x and z directions of the tunnel body. The vibrations of the anchor cables are decomposed into three directions, and the parameter excitation at the connection point between the anchor cables and the tunnel body is taken into account. The equations of motion for the three degrees of freedom of the anchor cables are established using Hamilton’s principle, and then the three equations are solved using the Galerkin method and the fourth-order Runge–Kutta method. The basic characteristics of an internal wave stratified flow acting on the anchor cables are considered, as well as the influence of the incident angle of the ocean currents on the three degrees of freedom of the anchor cables. The results indicate that (1) stratified flow weakens the first- and third-order vortex-induced vibrations of the anchor cables while enhancing the second-order vortex-induced vibrations. When considering the parameter excitation of the anchor cables, the first- and third-order vibrations are weakened, while the second-order vibration remains significant; (2) the first-order vibration of the anchor cables reaches its maximum value when the transverse oscillation frequency of the tunnel body is twice its natural frequency, and the second-order vibration of the anchor cables reaches its maximum value when the transverse oscillation frequency of the tunnel body is twice its natural frequency; (3) the downstream vibration of the anchor cables increases with the increase in the incident angle of the ocean currents, the cross-flow vibration of the anchor cables decreases with the increase in the incident angle of the ocean currents, and the axial vibration of the anchor cables reaches its maximum value when the incident angle of the ocean currents is 60 degrees; (4) stratified flow weakens the lock-in phenomenon of the anchor cables, and the influence of the 1/2 stratified flow on the vibrations of the anchor cables is greater than the influence of the 1/2 stratified flow.

Enhancing Cable Vibration Measurement at Long Distances Through Super-Resolution Reconstruction and Target Foreground Segmentation

This paper presents a comprehensive non-contact computer vision-based system for monitoring cable vibrations in cable-supported bridges, addressing challenges related to low image resolution and feature extraction difficulties at long distances. The proposed system utilizes deep learning techniques to enhance cable vibration recognition accuracy and offers a practical solution for cable monitoring without the need for target assistance. The core of the system is a novel two-stage model, which combines a super-resolution (SR) video reconstruction algorithm with state-of-the-art Resnet-34 and Swin-B models for precise target foreground segmentation. This approach significantly improves the recognition of target details and enhances the accuracy of cable vibration data in monitoring videos. Furthermore, a phase-based motion estimation (PME) algorithm is employed for precise cable vibration measurement. Field tests conducted on two cable-supported bridges validate the effectiveness of the system. The results demonstrate superior accuracy and noise immunity compared to traditional methods, achieving sub-pixel level precision with a maximum error rate below 2%. This system represents a significant advancement in non-contact structural health monitoring for long-distance cable vibration monitoring in cable-supported bridges.

Real-time identification of time-varying cable force for cable-stayed bridges based on vibration monitoring

Time-varying cable-force identification is fundamental for assessing the fatigue damage of stay cables. This study proposes a novel method for real-time time-varying cable force identification. This method updates the cable vibration signals through the sliding window and employs adaptive chirp mode decomposition (ACMD) to identify the instantaneous frequencies of the cables. Finally, the cable forces were calculated based on the taut string theory. The novelty of this study lies in the introduction of ACMD to enhance the accuracy of cable-force identification, while adaptively determining the key parameters of ACMD based on the scale space peak picking (SSPP) algorithm. The effectiveness of this method was been verified through numerical models, with the results showing that the maximum relative error in cable-force identification was 0.87%. Furthermore, this method was successfully applied to a sea-crossing cable-stayed bridge, demonstrating its ability to assess cable force accurately.