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 novel analytical method is proposed to solve the cable network system.•Dynamic axial forces are included to obtain more accurate results.•The dimension of the resulting characteristic matrix is small.•The dimension does not increase with the increase in the number of cross-ties.
•This paper proposed a deployment analysis method for soft cable networks from slack to tension with advantages in convergence, algorithm stability, easy operation, and high efficiency.•The proposed ...method can effectively capture cable networks’ time-varying slack/tension state with various topologies, deployment modes, and geometric dimensions.•The real-timely updated cable tension and node positions are available for the dynamic coupling with the soft cable network's supporting mechanisms.•The mapping relationship between the design parameters and the dynamic behaviors is discussed by analyzing the deployment process of cable networks.
Cable networks are widely used in space deployable devices and other fields for their large spans, lightweight, and small storage volumes. Among them, the deployable cable network usually turns from a stowed state to a fully deployed configuration and finally forms the working shape. The accurate and effective deployment analysis from slack to tension concerns the stable and efficient service of these cable networks. However, there are still no effective ways to analyze the deployment of cable networks with varying topologies and deployments modes. This paper proposed a general dynamic method for the deployment analysis of cable networks. The cable network is divided into a set of particles, and the deployment process is regarded as a series of time steps. Each node's equations about the force and displacement are formulated and assembled by applying a topological matrix to form the dynamic system model. The cable node's coordinates in the stowed state are calculated and further used to solve the coordinates and tension in the following time step by central difference method. Repeat this process until obtaining all the nodes’ positions and cable forces during the deployment. The cables’ slack/tension states are evaluated real-timely, and cable tension and node coordinates are updated accordingly, which makes the dynamic coupling with supporting mechanisms possible. The presented method applies to the deployment dynamic modeling and analysis of cable networks with various topologies, deployment modes, and geometric dimensions, with effective, easy operation, good convergence, and high-efficiency features.
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Offshore wind farms are increasingly becoming the focus of clean sources market because of the huge energy potential and fast-maturing technology. The existing researches normally optimize the wind ...turbine layout and two-dimensional cable routing independently. This work focuses on the synchronization optimization of site selection of the offshore wind farm, three-dimensional wind turbine layout and three-dimensional cable network routing based on meta-heuristic algorithms and geographic information systems. Several practical issues, i.e., restricted areas, power generation, cable network and energy loss, are taken into consideration. A two-layer model is proposed. The outer layer model is for the site selection and the wind turbine layout optimization. The inner layer model is for the obstacle-avoiding cable routing optimization. In this stage, the seabed terrain is considered for the first time. The proposed integrated model is complex and non-convex. Thus, a hybrid method including an improved ant colony optimization combined with genetic algorithm, dual-simplex method and Kruskal algorithm is proposed to search the solution more efficiently. The initialization stage of the hybrid method is improved from random assignment to directional assignment. The directional solution is obtained by the widely used genetic algorithm. A case study based on a real offshore wind farm is established to prove the effectiveness of the proposed methodology. The results show an over one million dollars increase in annual benefit compared with conventional methods.
The regular monitoring of cable forces is essential for ensuring the safety of cable structures both during construction and throughout their lifetime. This paper aims at developing a vibration-based ...identification procedure of the axial forces, bending stiffness, and, secondarily, the crossing point position of cable networks. A model constituted by two crossing stays having small bending stiffness and negligible sag effects is considered. The in-plane direct dynamic problem is solved both numerically and through a perturbation approach. The obtained results are compared to the outcomes of a finite element model for verification purposes. The theoretical studies are also supported by experimental tests performed on a real cable-stayed bridge (Haccourt bridge), which provide insights into the dynamics of the system showing that models of cables with small bending stiffness are more appropriate than taut string models. The inverse analysis based on non-linear Bayesian regression is developed and the closed-form asymptotic formulations are used to prove that the bending stiffness, the cable forces, and the crossing point position can be separately identified from a set of observed frequencies. The implemented procedure is then applied to the tested bridge as a proof of concept, showing that the proposed in-plane identification strategy provides satisfactory results.
•An optimization design method for cable network antennas is proposed to reduce the on-orbit thermal errors and relieve the burden of shape pre-adjustment before launch.•The thermal-structural model ...considering the thermal deformation and elastic deformation of the truss and cable network is established.•The antenna's uneven temperature filed at typical orbital positions is calculated, and the influences of the on-orbit thermal effects on the antenna surface accuracy and tension distribution are discussed.•Numerical examples are provided, and the results proved that the antenna's on-orbit surface accuracy and tension distributions were improved effectively by the optimization.
Cable network antennas are widely used in space missions, and high requirements on the reflector surface accuracy should be met to achieve reasonable electromagnetic performance. As the form of the cable network is dependent on forces and vice versa, the optimization design for the antenna's cable forces is extremely important. The current optimization methods are usually conducted under ambient temperature, ignoring the shape errors caused by the on-orbit thermal effects in space. Besides, the application of the active shape adjustment method is also limited by the on-orbit measurement and on-orbit control techniques at present. To reduce the on-orbit thermal disturbances and relieve the burden of shape pre-adjustment before launch, we proposed an optimization design method focusing on the on-orbit performances. The antenna's uneven temperature filed at typical orbital positions was calculated based on the heat radiation and conduction theories. The thermal-structural model considering the cable network's and the truss's thermal deformation and elastic deformation was established. For the optimization, the cable force densities were chosen to be the optimization variables, the antenna's shape errors at typical orbital positions were taken as the objectives, and the tension distributions at these orbital positions were considered as the constraint conditions. Numerical examples demonstrated that the proposed method improved the antenna's on-orbit surface accuracy effectively. This work provided ideas and solutions for the cable network's optimization design considering the on-orbit performances in the space environment.
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Cable-network antenna is regarded as one of the most ideal satellite antennas. In previous configuration design methods, some basic information including the node connectivity is usually not ...considered, which affects the subsequent analyses. Meanwhile, the existing form-finding methods mainly adapt to specific cable-network antennas with fixed configurations. Only the antenna accuracy or tension distribution is optimized, which usually cannot guarantee an optimal result. Here an integrated method both for the cable-network antenna's configuration and pretension design with varying topologies and parameters is proposed. Firstly, a parameterized configuration design approach is presented. The node coordinates are calculated by the design requirements, and the antenna topology is described by graph theory. Secondly, a pretension modeling approach is proposed. The parameterized equilibrium equation for the cable-network antenna with a flexible supporting truss is established. Thirdly, the original length approach for form-finding is proposed. Using this approach, a bi-objective optimization model is established to optimize both the antenna accuracy and tension distribution. Lastly, numerical examples are provided to verify the effectiveness of the proposed method, and the form-finding results are compared with the previous method.
Undersea cables play a crucial role in enabling global communication and data transfer, significantly affecting Internet speeds. Without them, global communication would be severely limited. As ...technology advances and network demands increase, the number and variety of optical fibers within cables are constantly increasing. This growth results in more costly cable networks with the ability to transmit more data and enhances the speed and reliability of data transmission. The construction of an undersea cable system requires careful consideration of the appropriate bandwidth of the cable to meet network bandwidth requirements while minimizing costs. In this article, we formulate the undersea cable network optimization problem taking account of the bandwidth capacity of each cable edge on the cable network as a weighted edges Steiner minimum tree problem and describe a new algorithm called the weighted edges Steiner minimum tree (WE-SMT) algorithm. For the given locations of the terminal nodes and the bandwidth capacity requirement, the WE-SMT algorithm optimizes the position of Steiner nodes, the bandwidth capacity of each cable edge, and the cable path. We implement our algorithm in a real-world setting, evaluating the benefit gained against the outcomes obtained without accounting for bandwidth optimization, as well as studying the effect of data resolution on the quality of the path planning results. In addition, we assess the performance of our new algorithm in comparison with that of an operational real-world cable system.
•Form finding and optimization method for flexible-supported cable nets is proposed.•The interactive effect is captured by solving the non-compatibility problem.•Linear form for the determination of ...free node coordinates is derived.•The method is applied to mesh reflector antennas to demonstrate the efficiency.
Cable network structures consist of the cable networks and supporting frames, and the whole structures form the equilibrium states under the interactions between them. The existing methods haven’t considered the flexibility of the supporting frames and thus fail to fully capture the interactive effect between cable networks and flexible frames in the design optimization. This leads to the deviations between the design results and the real equilibrium states. Here we propose a form finding and design optimization approach for cable network structures with flexible frames. By solving the non-compatibility problem between cable and beam elements (due to rotation DOF), the cable network and supporting frame can be coupled to accurately model the real equilibrium state in the optimization model. We also derive the linear form for the determination of the free node coordinates from systematic equilibrium equations, which greatly reduces the computing cost of the optimization design and makes the multi-variable optimization more achievable. The proposed approach is effective for the form finding and design optimization of flexible supported cable networks with high surface accuracy requirements and multiple design variables. It is applied to mesh reflector antennas, and case studies are provided to verify the effectiveness of the methodology.
•Proposed a cable network analytical model by considering cable sag and bending stiffness.•Sag has a more sizable impact on the modal frequency than cable bending stiffness.•Modal cross-over occurs ...in cable networks irrespective of cross-tie axial stiffness.•Modal cross-over in cable networks could occur between a global mode and a local mode.•Modal cross-over of a stiffer cable network is advanced to occur at a smaller sag.
Cross-tie solution is commonly employed to mitigate stay cable vibrations, especially the long ones. Therefore, cable sag could have a sizable impact on the dynamic response of the formed cable network and should not be neglected. Besides, the reduced cable effective length due to the installation of cross-ties and the larger diameter of longer cables would render the cable bending stiffness to have a more pronounced effect on the dynamic behavior of cable networks consisting long cables. Though the mechanism and effectiveness of cable networks have been studied by numerous researchers, majority of these work employed the taut cable assumption in modeling cable behavior. Only a few recent studies investigated the influence of either cable bending stiffness or cable sag separately on the modal response of cable networks, whereas the evaluation on their combined effect has yet to be fulfilled. In the current study, an analytical model of a flexible two-cable network proposed earlier by the authors is refined by including the sag effect. The combined effect of cable sag and bending stiffness on the dynamic behavior of cable networks with different configurations are examined, using the linear theory of shallow cables. Besides, the effect of cross-tie axial stiffness and installation location, as well as the length ratio and the bending stiffness ratio between the consisting cables, on the occurrence and characteristics of modal cross-over are discussed. Results show that while cable bending stiffness would influence all network modes, sag would only influence the symmetric modes. Both of them have a stiffening effect on the affected modes with that of the latter being more sizable, in particular, on the high order modes. Besides, modal cross-over in cable networks is observed to occur not only between two global modes, but also a global mode and a local mode. Enhance the stiffness of a cable network is found to advance the occurrence of modal cross-over at a smaller sag.
•Proposed a refined cable network analytical model by considering cable bending stiffness effect.•Assessed impact of cable bending stiffness on the modal behavior of cable networks.•Ignore cable ...bending stiffness would reduce network modal frequencies, especially high order ones.•Cable bending stiffness has more effect on local modes than on global modes.•Modal order is not affected by the presence of cable bending stiffness.
Cross-tie solution has proven to be effective in mitigating cable vibrations on cable-stayed bridges. In the formed cable network, the consisting cables are divided into shorter segments by cross-ties and thus significantly reduced their effective length. While bending stiffness plays an important role in the behavior of shorter cables, its effect has not been considered in any existing cable network analytical models. To assess the impact of cable bending stiffness on the in-plane dynamic response of cable networks, in the current study, an existing analytical model of a two-cable network is refined by taking into account the cable bending stiffness in the formulation. A set of closed-form solutions are derived to clearly reveal the impact of cable bending stiffness on the modal response of two-cable networks having different configurations. The proposed analytical model is validated by numerical simulations and the modal analysis results are compared with those of the corresponding taut-cable networks. It is found that the cable bending stiffness would influence all the modes of a cable network by increasing their modal frequencies, with the stiffening effect on the high order global and local modes being more considerable. If neglected, an underestimation of network fundamental frequency up to 7.1% could occur. Further, the cable bending stiffness has more effect on local modes than global modes. Some local modes could evolve into global modes. Nevertheless, the modal order is not affected by the presence of cable bending stiffness.
