Cable Stiffness Research Articles

Parameter Study and Optimization of Static Performance for a Hybrid Cable-Stayed Suspension Bridge

The hybrid cable-stayed and suspension (HCSS) bridge is known for its stability and cost-effectiveness, with significant application potential. This study examined the static performance of an HCSS bridge with a 1440 m main span. A finite element model (FEM) was developed to assess key parameters, such as the span-to-rise ratio, cable-to-hanger ratio, pylon stiffness, steel–concrete interface, and cable stiffness. Through FEM analysis and parameter optimization using the zero-order and first-order optimization methods in an ANSYS module, key design variables were optimized. The results show that an inappropriate span-to-rise ratio negatively impacts mid-span girder forces, while increasing the cable-stayed area enhances the overall stiffness. Main cable stiffness plays a crucial role in load-bearing and deformation control. Significant force differences were observed between stay and hanger cables, with axial force in the main girder increasing from the side span to the pylon under dead load. Bending moments in the transition region varied widely under combined loads. Optimizing parameters, such as the span-to-rise and cable-to-hanger ratios, significantly improved the mechanical performance of HCSS bridges, offering valuable insights for future designs.

A force-density framework for flexible multi-body dynamic analysis of clustered tensegrity structures

This paper develops a versatile and effective force-density framework for the flexible multi-body dynamic analysis of clustered tensegrity structures. In this framework, the force density is selected as the basic variable instead of force, and the clustered tensegrity structure is mathematically described in a vector and matrix form, encompassing topology, geometry, material, and force properties. A non-negative variable is defined as an indicator of the member stress state, and a complementary function is constructed to address the discontinuity issues that arise from the unidirectional axial stiffness of cables. Dynamic formulas are established within this force-density framework, with nodal coordinates selected as generalized parameters and formulations constructed in a matrix form. A complementary framework is established as an alternative for solving the dynamic equations, transforming the isolated steps of Newton’s iteration and cable state judgment (slack or tension) into a unified one, bringing more potential for improving solving efficiency. Numerical simulations are carried out to validate the approach, demonstrating that it effectively reveals the dynamic oscillation, tension changes, and cable slack behavior of clustered tensegrity structures during shape control. Comparative studies highlight the advantage of computational efficiency. The method proposed in this paper provides a robust mathematical model for studying clustered tensegrity structures, particularly regarding the shape control of deployable, active, and intelligent structures, aiding in understanding dynamic oscillation, tension changes, and cable slack behavior during their deformation. The methods can also be applied to cable net structures and other prestressed pin-jointed systems.

Experimental and numerical investigation on seismic performance of novel cable-restraining composite rubber bearings for highway bridges

Introducing cable restrainers into isolation bearings is promising to enhance the seismic performance of highway bridges. However, limitations exist in cost, performance, and analysis models of current products typically composed of flat sliding bearings (FBs) and separated cables. Therefore, this study proposes a novel cable-restraining composite rubber bearing (CRCRB) comprising a composite rubber bearing (CRB) as the bearing body and continuous cables. Cyclic tests were conducted on 12 specimens, including cable-restraining FBs and CRCRBs. Then, restoring force models of the bearing bodies were developed via theoretical analysis. Those of the cables were obtained from numerical models based on derived cable profiles. Finally, incremental dynamic analysis (IDA) was performed to evaluate the effects of the CRCRBs and cable models on structural responses. The test results verify the feasibility of the new cable layout and the advantages of the CRBs as the bearing body in restoring force, damping capacity, and residual displacement. As both the radii of the curved segments and the inclination angle of the linear one in the cable profiles decreased, the cable stiffness kept rising during loading. Cable sliding at clamps enlarged the cable-free displacement and residual deformation, and was relieved by adding clamps. The proposed models fit the test data well. The IDA results illustrate the superiority of the CRCRBs in mitigating bridge damage and highlight the importance of using the precise multi-linear cable model instead of the simplified linear one to avoid overestimating responses.

High performance of an innovative cable-in-conduit conductor with CWS cable pattern

Cable-in-conduit conductors, known as CICCs, were developed for constructing superconducting coils in tokamak fusion reactors. To achieve large currents in high magnetic field, CICCs were utilized with a short-twist-pitch (STP) cable pattern to prevent irreversible performance degradation, but also inducing higher AC losses. Institute Of Plasma Physics Chinese Academy Of Sciences (ASIPP) designed and manufactured three innovative CICCs, all featuring CWS (copper wire with a STP wound around superconducting strands with a long-twist-pitch) structure to increase both the current density and structure stiffness of CICC cable. These CICCs had the same new CWS cable pattern but the Nb3Sn superconducting strands were from different suppliers. All samples were subsequently tested under electromagnetic cycling tests in SULTAN. For similar electromagnetic performance degradation, the Lorentz load threshold of the CWS cable pattern exhibited to be higher than that of STP cable pattern. Moreover, the AC losses of CWS were 15% lower than that of STP cable pattern for low frequencies of the applied alternating magnetic field. Both results indicated that the CWS cable pattern has a higher margin of engineering safety and lower AC losses than STP cable pattern under the target operating conditions. This provides new insights in finding solutions for optimizing the CICCs’ cable pattern and preventing its electromagnetic performance degradation.

Study on Dynamic Characteristics of Long-Span Highway-Rail Double-Tower Cable-Stayed Bridge

The long-span dual-purpose highway-rail double-tower cable-stayed bridge has the characteristics of a large span and large load-bearing capacity. Compared with the traditional cable-stayed bridge, its wind resistance and seismic resistance are weaker, and the dynamic characteristics of the bridge are closely related to the wind resistance and seismic bearing capacity of the bridge. This study investigated the influence of the variations of bridge member parameters on the dynamic characteristics of the bridge and then improved the dynamic characteristics of the bridge. To provide the necessary experimental theory for the research work of the long-span dual-purpose highway-rail double-tower cable-stayed bridges, this paper takes the world’s longest span of the dual-purpose highway-rail double-tower cable-stayed bridge as the background, using the finite element analysis software Midas Civil 2022 v1.2 to establish a three-dimensional model of the whole bridge by changing the steel truss beam stiffness, cable stiffness, pylon stiffness, and auxiliary pier position, as well as study the influence of parameter changes on the dynamic characteristics of the bridge. The results show that the dynamic characteristics of the bridge can be enhanced by increasing the stiffness of the steel truss beam, the cable, and the tower. The stiffness of the steel truss beam mainly affects the transverse bending stiffness and flexural coupling stiffness of the bridge. The influence of cable stiffness is weak. The tower stiffness can comprehensively affect the flexural stiffness and torsional stiffness of the bridge. The position of auxiliary piers should be determined comprehensively according to the site conditions. In practical engineering, the stiffness of components can be enhanced according to the weak links of bridges to improve the dynamic characteristics of bridges and save costs.

Design and Experimentation of Tensegrity Jumping Robots

Jumping robots possess the capability to surmount formidable obstacles and are well-suited for navigating through complex terrain environments. However, most of the existing jumping robots face challenges in achieving stable jumping and they also have low energy utilization efficiency, which limits their practical applications. In this work, a two-module jumping robot based on tensegrity structure is put forward. Firstly, the structural design and jumping mechanism of the robot are elaborated in the article. Then, dynamic models, including the two modules’ simultaneous jumping and step-up jumping process of the robot, are established utilizing the Lagrange dynamic modeling method. On this basis, the effects of parameters, including the stiffness of elastic cables and the initial tilt angle of the robot, on the jumping performance of the robot can be obtained. Finally, simulations are carried out and a prototype is developed to verify the rationality of the tensegrity-based jumping robot proposed in this work. The experiment results show that our jumping robot can achieve a stable jumping process and the step-up jumping of each module of the prototype can have higher energy efficiency than that of simultaneous jumping of each module, which enables the robot a better jumping performance. This research serves as a valuable reference for the design and analysis of jumping robots.

Damping effects of a stay cable attached with a viscous damper and a high damping rubber damper considering cable bending stiffness and damper support flexibility

To mitigate cable oscillations in cable-stayed bridges, a common approach involves using a strategically positioned viscous damper near the cable’s anchorage and bridge deck. However, for longer cables, this method may be insufficient due to installation constraints. In such cases, supplementing the damping system with a high-damping rubber (HDR) damper near the cable’s anchorage point on the bridge tower becomes imperative to enhance the cable’s damping ratio. Conventional designs often overlook crucial factors like viscous damper support stiffness and stay cable bending stiffness when integrating dampers into cable-stayed structures. This study presents findings on achieving an effective damping ratio in stay cables by using both a viscous damper and an HDR damper, considering the influence of viscous damper support stiffness and stay cable bending stiffness. The results indicate that the combined deployment of these dampers achieves a damping efficiency approximately equivalent to the sum of their individual effects. Importantly, decreased viscous damper support stiffness significantly affects the damping effectiveness, leading to a rapid decline in the stay cable’s damping ratio. While stay cable bending stiffness also influences the damping ratio, its impact is relatively less pronounced than that of viscous damper support stiffness. The study outcomes enable a more accurate prediction of the achievable damping ratio for a stay cable with additional components, considering both damper support stiffness and stay cable bending stiffness. Furthermore, the study explores parameters of both the viscous damper and HDR damper, such as the viscous coefficient, loss coefficient, HDR damper stiffness, and damper placement, evaluating their influence on the first damping ratio of the stay cable. The survey results provide valuable insights for determining optimal parameters for both dampers, maximizing the damping efficiency of cable-stayed bridges.

Practical Formulae for Estimating Cable Tension with Unknown Rotational Restraints by the Frequency Method

To calculate the tension in cables with different boundary conditions, the relationship between cables with fixed–fixed and hinged–hinged boundary conditions in terms of the frequency was determined according to frequency characteristic equations of cables with the two boundary conditions. In this way, a simple calculation formula for tension with fixed–fixed boundary conditions was deduced. Similarly, a calculation formula for the tension in cables with a fixed–hinged boundary condition was proposed using the method. Results show that the proposed formulae, with high computational accuracy and wide ranges of application, can be used to calculate the cable tension under a dimensionless parameter (ξ) not lower than 6.9, so it is convenient to apply the formulae to calculate tension in practice. Meanwhile, changes in the frequency ratios of cables with different boundary conditions than those with a hinged–hinged boundary condition were analyzed. Results show that when ξ is not lower than 25, the frequency ratios of cables of various orders tend to be the same. The boundary coefficient(λ) was introduced. Given the cable stiffness, the tension and boundary coefficient(λ) can be calculated through linear regression. The method considers influences of unknown rotational end-restraints of cables and accurately calculates the cable tension. By using simulation examples and engineering examples, the method was verified to be accurate in calculating the cable tension, thus providing a novel, practical method for estimating tension in cables, booms, and anchor-span strands of suspension bridges.

Nonlinear static solution of suspension bridge formulated from a surrogate model with secant stiffness of suspension cables

Explicit analytical solution may offer great convenience for the design and parametric study of suspension bridges. However, the nonlinear behavior of suspension cable exacerbates the difficulty of such theoretical derivation. Adopting secant stiffness is an effective way to deal with the nonlinearity of the cable, but the crux is how to find its deformed state under external loading. The strategy of this study is primarily targeted at a typically arranged three-span suspension bridge. It starts from formulating the basic form of nonlinear stiffness of suspension cables by setting the elastic stiffness and geometric stiffness in series, then a surrogate model is accordingly established with the nonlinear springs to replace the mid-span and side-span cables. The deformed state of the surrogate model subjected to the specified external load cases will be found by restricting and releasing its tower tops, and thus the analytical formula of the secant stiffness can be obtained. Consequently, the nonlinear static solution of suspension bridge, including force and deformation changes in the cables and towers, can be explicitly expressed with the secant stiffness. The general solution procedure can also be extended to multi-span suspension bridges. Finally, the nonlinear static solution is verified by numerical examples of a three-span suspension bridge and a four-span suspension bridge. The parametric analysis reveals that the nonlinearity of suspension bridge will become significant as the side-span to mid-span ratio increases, or when the side-span cables are hung with hangers.

An all-position type control strategy of the haptic interactive virtual training system based on cable-driven

The virtual microgravity training system based on cable drive usually uses a force-position hybrid control strategy which has following problems: the force control method is sensitive to load disturbances, variable stiffness characteristics of cables reduce the control accuracy of PID controllers, and the expected tension fluctuations are large. These will affect the control accuracy, and further affect the tactile sensation and training effectiveness of astronauts. For the above problems, an all-position type control strategy is proposed to improve the system control accuracy. This strategy uses a compliant control method. In this method, elastic elements are connected in cables, the conversion model of tension and displacement is established, and the tension control is realized by the displacement control which has characteristics of high control accuracy and strong resistance to load disturbance. The PID controller is replaced by the active disturbance rejection controller. In this controller, the tracking differentiator is used to reduce high frequency noises of the input signal, and the extended state observer is used to estimate and compensate the error caused by the change of the cable stiffness. A tension distribution method is designed to make expected cable tensions approach the average tension to reduce the tension fluctuation. The experimental results show that compared with the force-position hybrid control strategy, the all-position type control strategy reduces the tension error and speed error by about 51% and 33% respectively.

Numerical assessment and characterization of automobile high-voltage cable coverings

In the automotive industry, arranging wire harnesses in assembly plants requires manual work. The stiffness of the high-voltage cable implies that personnel applies sufficient force on the cable to achieve a proper installation. Sometimes, the applied force is not strong enough; thus, the cable is not properly installed, or the personnel gets injured, raising ergonomic concerns that need attention. The challenges arise from the intrinsic cable characteristics such as diameter, copper type, cable strand quantity, first-layer insulator, cable insulator glue, and protective covering. The primary objective of this research is to examine how various factors, such as cable length and protective covering, impact the mechanical properties that influence the assembly of high-voltage cables. The methodology proposed consisted of characterizing the mechanical properties of the high-voltage cables in a cantilever beam test to measure deflection in response to an applied force. The measured properties were contrasted through a Finite Element Analysis of the high-voltage cable. The results validated the initial hypothesis, revealing two key findings. Firstly, the stiffness of cables varies with increasing length. Secondly, cables with tape exhibit greater stiffness than those with conduit and cables without covering, as detailed in the results section. In conclusion, extending cables without attachment points is recommended until the interfaces and environment permit. Furthermore, minimizing tape for cable protection while exploring alternative safeguards can enhance stiffness and facilitate an ergonomic installation assembly under favorable conditions. This study contributes valuable insights for optimizing high-voltage cable installation processes in assembly plants, addressing stiffness concerns through informed choices and design considerations.

Joint Identification of Cable Force and Bending Stiffness Using Vehicle-Induced Cable–Beam Vibration Responses

Joint Identification of Cable Force and Bending Stiffness Using Vehicle-Induced Cable–Beam Vibration Responses

Analytical Estimation and Experimental Validation of the Bending Stiffness of the Transmission Line Conductors

The bending stiffness of transmission line conductors can vary significantly, ranging from maximum stiffness when behaving monolithically to minimum stiffness when wires behave loosely. This large range makes it challenging to estimate stiffness accurately at intermittent bending stages. To address this issue, a mathematical model that accounts for both frictional forces between wires in the same layer and the clenching effects of helical wires from preceding layers is proposed in this paper. The proposed model estimates cable bending stiffness as a function of axial load and curvature for multilayered strands by considering slip caused by wire behavior. To evaluate the bending stiffness, experiments were conducted on Panther and Moose Indian Power Transmission line conductors. The proposed slip model considers Coulomb frictional effects and clenching effects caused by Hertzian contact forces, filling the void in the estimation procedure. Additionally, the model considers the wire stretch effect, a parameter not previously accounted for in cable research. The predicted numerical results of the proposed model were found to vary within a maximum of 7% from the experimental tests. The proposed mathematical model thus offers a more accurate and comprehensive way of estimating the bending stiffness of transmission line conductors, addressing the existing limitations in the estimation procedure.

Comprehensive stiffness regulation on multi-section snake robot with considering the parasite motion and friction effects

Snake robots have been widely used in challenging environments, such as confined spaces. However, most existing snake robots with large length/diameter ratios have low stiffness, and this limits their accuracy and utility. To remedy this, a novel ‘macro-micro’ structure aided by a new comprehensive stiffness regulation strategy is proposed in this paper. This improves the positional accuracy when operating in deep and confined spaces. Subsequently, a comprehensive strategy for regulating the stiffness of the system is then developed, along with a kinetostatic model for error prediction. The internal friction, variation of cable stiffness as a function of tension, and their effects on the structural stiffness of the snake arm under different configurations have been incorporated into the model to increase the modelling accuracy. Finally, the proposed models were validated experimentally on a physical prototype and control system (error: 4.3% and 2.5% for straight and curved configurations, respectively). The improvement in stiffness due to the adjustment of the tension in the driving cables (i.e. average 183.4%) of the snake arm is shown.

A novel identification approach of mesh reflector based on tie cable tension sensing

The mesh reflector suffers inevitably from complicated environmental interferences during long-term on-orbit operation and consequently the reflector may deviate significantly from its initial state. It is thus crucial to identify the deformed reflector on-orbit in order to evaluate timely the mesh reflector accuracy. However, the existing reflector identification methods are difficult to achieve this object as the most of them need to install additional equipment on antenna or satellite. Aiming at realizing on-orbit mesh reflector identification, a novel identification approach based on tie cable tensions sensing (TCTS) is proposed in the paper. The TCTS method leverages real-time measurements of tie cable tensions through embedded force sensors to calculate the remaining cable tensions required to address reflector deformations. For this purpose, an optimization problem is established based on tension balance equation and then solved using a proposed iteration solution algorithm incorporating the genetic algorithm. The actual configuration of mesh reflector is then determined by all cable tensions according to the force density method and the reflector can be identified ultimately. The simulated studies on reflector identification of a mesh reflector with 8 m aperture diameter are conducted under temperature loads and cable stiffness degradations respectively. The results indicate that the TCTS method possesses high reflector identification accuracy and good anti-noise capability under different environmental interferences. Furthermore, a reflector identification method based on partial tie cable tensions sensing (PTCTS) is developed in order to reducing system complexity and cost. The sensitivity analyses of tie cable tensions are performed in order to provide a reference for location placement of force sensors in the PTCTS method. The simulated results indicate that the optimized location placement scheme can enhance significantly the reflector identification accuracy of PTCTS method. Besides, the PTCTS method exhibits equal anti-noise capability with the TCTS method. Finally, the experimental studies are conducted on reflector identification of a mesh reflector test model with 1.5 m diameter and 0.5 m height under cable stiffness degradations. Through comparing with the reflector identification results obtained by the photogrammetry method under different cable stiffness degradation degrees, the accuracy and effectiveness of the TCTS/PTCTS methods are demonstrated experimentally.

Damping in stay cable with damper: Practical universal damping curve and full-scale measurement

This paper includes two main parts which are the development of a universal damping curve for cables of cable-stayed bridges with dampers and a full-scale measurement of cable damping. In the first part, the universal damping curve is derived for cables with viscous dampers or High Damping Rubber (HDR) dampers. The proposed damping curve is a single curve which incorporates several cable-damper parameters like cable bending stiffness, boundary conditions at cable ends (hinged, fixed or restraint ends), damper stiffness, damper support stiffness and added negative stiffness. A numerical approach by a finite difference method (FDM) is also developed to verify the proposed universal damping curve. In addition to FDM, the accuracy of the proposed curve was confirmed with damping formulations in literature over ten different damper types. The results showed a good agreement of estimated damping between proposed damping curve and others. Additionally, a significant improvement in estimating cable damping was observed through two available full-scale tests, which compared the results between proposed curve and current curve. The second part in this study presents a full-scale measurement of cable vibration and a real application of the proposed damping curve for the identification of damping in cables of Shinminato Bridge (cable lengths from 100 to 200 m). Both HDR and viscous dampers were used for the cable vibration control of the bridge. The results of damping analysis indicated that the HDR damper effectiveness was higher than 0.7 whereas this effectiveness was smaller than 0.4 for the viscous damper.

A novel method for frequency analysis of a small wind turbine with tubular guyed tower: An experimental evaluation

The present study sets out a novel methodology for the theoretical and experimental analysis required to find the natural frequencies of a small wind turbine with a guyed tower. These frequencies may cause resonance phenomena when occurring close to each other. These phenomena require precise mathematical models and experimental analysis to facilitate structural design calculations. The method uses a life-sized commercial turbine mounted on a fold-down guyed tower, the Rayleigh-Ritz numerical method, vibration modes, blade frequency, and cable stiffness. In addition, cable stiffness value depends on various factors, such as diameter, longitude, and materials. The results reveal that it is possible to shift the fundamental frequency of the cable and its harmonics. The cable is the main element that may cause resonances in other elements of the small wind turbine with a tubular guyed tower due to the range of frequencies that can be adopted depending on the cable tension. Finally, the results show a reasonable concordance between the values for the natural frequencies calculated by the mathematical model and the experimental values, obtaining an error of lower than 3.43% for the fundamental frequency system.

Optimization of Extradosed Bridge and Analysis of Parameters' Sensitiveness as a Case Study on Abay Bridge

AbstractThe paper describes analytical sensitivity analysis and structural optimization for Abay extradosed cable‐stayed bridge. Identify significant design variables using sensitivity analysis by considering cable stiffness, girder weight and stay cable tension force. The aim of the study is weight minimization of superstructure components of Abay bridges. It has span length (100+180+100) m. For structural optimization, it was carried out by taking total material weight of girders, pylon and stayed‐cable as an objective function and all requirements of strength, stability, serviceability, and fatigue as constraint functions. The formulated optimization problem was coded into Matlab R2019a software and analysis results are retrieved from MIDAS CIVIL 2019 software. The paper gives more reduced weight of bridge from conventional design output by using same material grade. The result shown that optimum stay cable length was reduced from conventional design output by 10% from total values, optimum design of pylon height reduced weight of conventional design by 20.03% and optimum design of box girder reduced girder weight by 19.47%.

Functional significance of lamellar architecture in marine sponge fibers: Conditions for when splitting a cylindrical tube into an assembly of tubes will decrease its bending stiffness

Numerous ingenious engineering designs and devices have been the product of bio-inspiration. Bone, nacre, and other such stiff structural biological materials (SSBMs) are composites that contain mineral and organic materials interlaid together in layers. In nacre, this lamellar architecture is known to contribute to its fracture toughness, and has been investigated with the goal of discovering new engineering material design principles that can aid the development of synthetic composites that are both strong and tough. The skeletal anchor fibers (spicules) of Euplectella aspergillum (Ea.) also display a lamellar architecture; however, it was recently shown using fracture mechanics experiments and computations that the lamellar structure in them does not significantly contribute to their fracture toughness. An alternate hypothesis—the load carrying capacity (LCC) hypothesis—regarding the lamellar architecture’s functional significance in Ea. spicules is that it enhances the spicule’s strength, rather than its toughness. From an ecology perspective the LCC hypothesis is certainly plausible, since a higher strength would allow the spicules to more firmly anchor Ea. to the sea floor, which would be beneficial to it since it is a filter feeding animal. In this paper we present support for the LCC hypothesis from a solid and structural mechanics perspective, which, compared to the support from ecology, is far harder to identify but equally, if not more, compelling and valid. We found that when the spicule functions in a knotted configuration a reduced bending stiffness benefits its load carrying capacity and that sectioning a cylindrical tube into an assembly of co-axial tubes can reduce the tube’s bending stiffness for a wide class of materials that are consistent with the spicules’ axial symmetry. The mechanics theory developed in this paper has applications beyond providing support for the LCC hypothesis. For example, it makes apparent many design strategies for reducing the bending stiffness of large industrial cables (e.g., undersea optical data transmission cables) while maintaining their tensile strength, which has benefits towards the handling, storage, and transportation of such cables.

How the Material Characteristics of Optical Fibers and Soil Influence the Measurement Results of Distributed Acoustic Sensing.

Fiber optic distributed acoustic sensing (DAS) technology is widely used in security surveillance and geophysical survey applications. The response of the DAS system to external vibrations varies with different types of fiber optic cable connections. The mechanism of mutual influence between the cable's characteristics and DAS measurement results remains unclear. This study proposed a dynamic model of the interaction between the optical cable and the soil, analyzed the impact of the dynamic parameters of the optical cable and soil on the sensitivity of the DAS system, and validated the theoretical analysis through experiments. The findings suggest that augmenting the cable's bending stiffness 5.5-fold and increasing its unit mass 4.2-fold result in a discernible reduction of the system's response to roughly 0.15 times of its initial magnitude. Cables with lower unit mass and bending stiffness are more sensitive to vibration signals. This research provides a foundation for optimizing vibration-enhanced fiber optic cables and broadening the potential usage scenarios for DAS systems.