Behavior Of Cables Research Articles

Nonlinear Parametric Resonance Behavior of Cables in a Long Cantilever Bridge for Sightseeing Platform

In order to study the parametric vibration of stayed cables in a long cantilever bridge for a sightseeing platform, nonlinear parametric vibration equations of the stayed cables excited by the vibration of bridge deck and tower are derived. Then, a second‐order differential equation is transformed into a first‐order ordinary differential equation, which is solved by using the Runge–Kutta method. A finite element model of cables was also built to verify the solution of the Runge–Kutta method. Then, the inherent dynamic characteristics of the full structure and all the cables with different lengths were analyzed to discuss the potential risk of parametric vibration. The longest and shortest cables were taken as examples to explore their nonlinear vibration performance. The effects of damping ratio, excitation position, and amplitude on cables’ nonlinear vibration performance were investigated. The results show that it will be more efficient and convenient to use the Runge–Kutta method to calculate cables’ nonlinear vibration amplitude without loss of accuracy. In addition, short cables have more resonance zones compared to long cables. Especially, with the cable length shortening, the dominant frequencies of the dynamic response and its amplitude increase significantly, and the number of resonance zones also increases. However, excessive excitation amplitude will also cause multiple resonance zones in the cable. The parametric analysis results show that it is effective and efficient to mitigate the nonlinear vibration by adjusting the frequency relationship between the bridge and the cables, rather than by increasing the damping ratio.

In-plane modal responses of two-cable networks considering cable bending stiffness effect

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.

Efficient modelling of flexible cable-pulley systems

This article proposes a universal procedure for efficiently modelling the flexible behaviour of pre-stressed cables, guided by multiple pulleys. Such cable-pulley systems usually connect various structural components, which often feature additional flexibility. One concern in holistic system analyses is to correctly describe the elasticity of the entire assembly for one particular spatial configuration. This can be achieved in terms of a linear stiffness matrix that accounts for the kinematics of the assembly. In this article, parametric stiffness matrices for arbitrary cable-pulley arrangements are derived. A reduction scheme is used to facilitate the integration of the derived stiffness matrix into superordinate finite element models. The method is validated with a non-linear finite element model and applied to a complex hoisting cable system connecting multiple large steel structures.

Electromagnetic Shielding Performance Measurement for Braided-Shield Power Cables at Low Frequency Regimes

Abstract Although various measurement techniques have been applied to both qualitative and quantitative evaluation for the electromagnetic shielding performance of braided-shield power cables, the existing measurements cannot directly assess the low-frequency shielding performance (typically below 100 kHz) due to factors such as ground-loop effects and dynamic range problem in measurement. To solve these, an improved shield reduction factor method, based on gain (T/R) rather than scattering parameters, is proposed to evaluate the shielding performance of braided-shield power cables from 25 Hz to 1 MHz. In this work, we highlight the implementation of measurement setup to avoid the effects of ground-loop and stray electromagnetic field. Meanwhile, the test cell is simplified according to the definition of the shield reduction factor in order to obtain the gain (T/R) parameters, which can be used to calculate transfer impedance as well. From the measurements we present more intuitive evaluation of shielding behavior of braided-shield power cables at low frequency regimes, and showcase a detailed comparative discussion between transfer impedance and shield reduction factor. The proposed shield reduction factor method is expected to be a useful way for the evaluation of the low frequency shielding performance of braided-shield cables.

Equivalent Axial Stiffness of Horizontal Stays

Cable-stayed structures are widely employed in several fields of civil, industrial, electrical and ocean engineering. Typical applications are cable-stayed building roofs, bridges, guyed masts, overhead electrical lines, and floating device anchorages. Since the cable behavior is often highly nonlinear, suitable equivalent mechanical cable models are often adopted in analyzing this kind of structures. Usually, like in the classical Dischinger’s approach, stays are treated as straight rods offering an equivalent axial tangent stiffness, so that each of them can be substituted with an appropriate equivalent nonlinear spring or truss element. Formulae expressing equivalent stiffness provided by classical methods are satisfactory only when the cable is highly stressed, and therefore its sag is small with respect to its chord; on the contrary, when the cable is slack, they give often contradictory or meaningless results. Aiming to remove that limitation, a more refined approach based on the application of the virtual work principle is discussed. Important products of that original rational criterion are accurate and closed form innovative expressions of the tangent stiffness of the cable, whose field of application is independent on the sag to chord ratio of the cable, as well as on the magnitude of the normal stresses. Referring to some relevant case studies, the results obtained applying these new formulae are critically discussed for cables made of different materials, also in comparison with the approximate expressions provided by simplified methods.

Evaluation of Thermal State for Underground Power Cables in Nasiriya City

Due to the increase in demand for electric power and increasing population density in different regions, the application of underground cables has become widely used in transmission and distribution networks. In this paper, the thermal behavior of underground cables was studied numerically. Four types of underground cables were selected copper conductor cables with (95 mm2) and (240 mm2) and aluminum conductor cables (95mm2) and (240mm2), which are used in the power networks in Iraq. The study was carried out based on the conditions surrounding such as the ambient temperature, the thermal properties of the soil and the current capacity, its effect on the thermal behavior of the cables. The results of the numerical simulation showed that the surrounding factors and loading capacities have a direct effect on determining the temperature of the cable. In addition, the type and size of the conductor cable material have an effect on determining the current-carrying capacity of the cable where the conductor cable with a nominal cross-sectional area 240mm2 has a temperature higher than the conductor cable with nominal cross-sectional 95mm2by (8.96%) for the copper conductor and (13.68%) for the aluminum conductor at current 500A.

Development of a test method and experimental study on cable unwinding

In addition to the textile industry, unwinding of cable or fiber is used in various fields such as electronics, communication, and guided weapons. The cable released from the package exhibit a complicated behavior, entailing a combination of rotational and translational motion. This causes problems such as entangling and fracture. Therefore, it is necessary to study boundary and adhesion conditions to prevent unwinding failure. In this study, an experimental device for the analysis of cable unwinding was developed, and unwinding behavior was analyzed experimentally under various unwinding conditions. The experimental device comprises a jig for high-speed camera measurements, control device, and cable unwinding device. Cable behavior was analyzed according to the unwinding velocity and the distance between the fiber package and the point where the fiber was released. In addition, unwinding behavior with respect of the tension acting on the cable was analyzed experimentally by applying the adhesive.

Corrosion Behavior of Different Cables of Large-Span Building Structures in Different Environments

AbstractSpiral strands, galvanized steel wires, galvanized semiparallel wire strands, and steel tie rods in large-span building structures are inevitably corroded due to long-term exposure to corro...

On the nonlinear effects of the mean wind force on the galloping onset in shallow cables

The critical aeroelastic behavior of horizontal, suspended, and shallow cables is analyzed via a continuous model accounting for both external and internal damping. Quasi-steady aerodynamic forces are considered, including their stationary contribution (mean wind force). This latter induces a rotation of the cable (steady swing) around the line connecting the suspension points, together with a deformation of the initial equilibrium profile under self-weight. First, by using perturbation methods, the nontrivial equilibrium configuration is analytically determined as a nonlinear function of the wind velocity. Then, the wind critical values at which bifurcations take place and the corresponding modal shapes are determined by solving a boundary value problem in the complex field. Numerical investigations are carried out to validate the perturbation solution. A preliminary nonlinear galloping analysis is also performed to verify the galloping onset in terms of non-trivial equilibrium path and critical modes. The nonlinear terms related to the fundamental path, from which bifurcations take place, play a key role revealing new insights. They are able to heavily influence the system bifurcation, making unstable configurations which instead would be aerodynamically stable without considering the effect of the mean wind force.

Nonlinear Dynamic Analysis of Transmission Line Cables under Synoptic Wind Loads

AbstractThis paper presents the structural behavior of transmission line cables under nondeterministic dynamic wind loads (atmospheric turbulence), considering aerodynamic damping and geometric non...

Comparative thermal decomposition characteristics and fire behaviors of commercial cables

The decomposition and fire behaviors of two commonly used cables were studied by a calorimeter. The effects of the cable type, the incident heat flux, and the thermal aging on the fire characteristics were specially analyzed. Two cables showed almost the same ignition property considering the same sheath material, and the thermally thick model for both cables was identified. The changes in mass and heat release between two cables presented a significant difference. This was ascribed to the different compositions and the structures of the cables. The theoretical derivation and experimental data fitting indicated that two cables gave a different fire risk. The fire hazard was greatly promoted under higher incident heat flux because more combustible compositions decomposed contributed to heat release. The ignition time of two cables first changed slowly with the thermal aging degree and then increased sharply, with a critical aging time of 30 days. The changing trends of mass and heat release with the thermal aging degree between two cables were significantly different, which was attributed to the different compositions of cable insulation, resulting in the different thermal aging mechanisms. This work may provide an in-depth understanding of fire behaviors of commercial cables.

Dynamic modeling of a radially multilayered tether cable for a remotely-operated underwater vehicle (ROV) based on the absolute nodal coordinate formulation (ANCF)

This research is aimed at the accurate modeling of an ROV's tether cable with a radially multilayered circular cross-section. In the coupled motion analysis of an ROV-tether system, dynamic modeling of a numerical tether continuum, which can accurately reproduce the nonlinear motion behavior of a flexible cable, is crucial since the tether motion greatly affects the ROV's stability. To this end, a new tether cable element based on the multilayered modeling approach is developed. To deal with the inconsistency of the tether's cross-section, the integration domain on the cross-section is divided into subdomains to account for different material properties in each layer and an accurate representation of the tether's cross-section. A Kelvin-Voigt model is employed to account for the viscoelastic behavior of the inner matrix, while nearly incompressible Mooney-Rivlin model is applied for the outer sheath. Structural weakening parameters are applied to modify the beam's strain energy. A new approach for analytical determination of dissipation factors for dilatational and deviatoric responses is proposed. Through validations against the numerical studies and experiment, the effectiveness of the proposed tether cable element is verified.

Effect of frequency-dependent soil parameters on wave propagation and transient behaviors of underground cables

This paper investigates the influence of frequency-dependent (FD) soil parameters in comparison to the constant soil (CS) parameters on wave propagations and transient characteristics of underground cables. Various FD soil models are summarized, and the calculated results of the FD soil parameters are compared with independent measured FD soil data. Longmire / Smith (LS) model is found to show the best agreement with the measured results. The frequency responses of wave propagations on underground cables are studied by the recently proposed extended transmission line (TL) approach together with the CS and the LS FD soil models. Calculated transient responses show more attenuation with a large soil resistivity at 100 Hz in comparison with those with a small soil resistivity at 100 Hz. Further, the transient voltage responses of a cross-bonded cable are compared with the transients solved by the Cable Constants and the existing FD soil routine in an EMT-type simulation tool, and a significant difference is observed.

Determination of Additional Tension in Towed Streamer Cable Triggered by Collision with Underwater Moving Object

Abstract The paper deals with issues connected with the behaviour of a streamer cable towed by a survey seismic vessel when the cable undergoes a strike triggered by collision with an underwater moving object. The consequences of such collisions may be both threat to the life of marine animals or damage to underwater units and large economic losses suffered by vessel owners. The risk of such collisions has increased over the last years as a result of increased offshore seismic survey operations. Therefore, a towed streamer should be very robust. To assure its robustness, we should know the deformation mechanism of a single streamer cable. This in turn requires the development of an appropriate mathematical model of such a phenomenon. In particular, the paper presents the characteristics of seismic survey vessels and streamers; an analysis of collisions that have occurred in the past; a statement of the problem, and a computer-aided system supporting simulation of the cable behaviour. To obtain all the necessary design parameters regarding the deformation mechanism of a streamer cable, we set up a dedicated computer-aided system that supports their calculation.

A new model for suspension bridges involving the convexification of the cables

The final purpose of this paper is to show that, by inserting a convexity constraint on the cables of a suspension bridge, the torsional instability of the deck appears at lower energy thresholds. Since this constraint is suggested by the behavior of real cables, this model appears more reliable than the classical ones. Moreover, it has the advantage to reduce to two the number of degrees of freedom (DOF), avoiding to introduce the slackening mechanism of the hangers. The drawback is that the resulting energy functional is extremely complicated, involving the convexification of unknown functions. This paper is divided in two main parts. The first part is devoted to the study of these functionals, through classical methods of calculus of variations. The second part applies this study to the suspension bridge model with convexified cables.

Influence of Oxygen Diffusion on Thermal Ageing of Cross-Linked Polyethylene Cable Insulation.

Thermal ageing of cross-linked polyethylene (XLPE) cable insulation is an important issue threatening the safe operation of power cables. In this paper, thermal ageing of XLPE was carried out at 160 °C in air for 240 h. The influence of oxygen diffusion on thermal ageing of XLPE was investigated by Ultraviolet–visible spectrophotometer (UV–Vis), tensile testing, and Fourier transformed infrared spectroscopy (FTIR). It was observed that the degradation degree not only depended on ageing time but also on sample positions. The thermally aged samples were more oxidized in the surface region, presented a darker color, more carbon atoms appeared in the conjugate cluster, had smaller elongation at break and tensile strength, and a larger carbonyl index. As ageing time increased, the non-uniform oxidation of the XLPE samples became more prominent. The degree of non-uniform oxidation caused by oxygen diffusion was quantitatively studied by first order oxidation kinetic. The calculated results demonstrated that carbonyl index measured by FTIR was more sensitive to non-uniform oxidation with a shape parameter in the range of 1–2. The result shown in this paper is helpful for interpreting and predicting the non-uniform ageing behavior of high voltage XLPE cables.

High Frequency Design and Analysis of Long Power Cable Inverter Fed Induction Motor Drive Method

Industrial applications call for a long interconnected cable between Adjustable frequency drive (AFD) and. The distributed inductance and the capacitance associated with the wire and the coupling between the wires within the cable, generates overshoot voltage due to the high rate of rise motor or fall of the high frequency PWM output of the AFD. It may result in damage to either motor or the AFD. In this study, a high regularity model of the cable is developed to predict and analyze the role of the cable in the generation of voltage transients. The future method is confirmed on untried setup test bench of 5HP induction motor and 100 meter power cable run along AFD system. The motor reflected overshoot voltage is estimated by the planned model in good conformity with the trial measurements results. The cable behavior is analyzed on parameters in occurrence domain as well as moment field for a three core cable in terms of their equivalent circuits. The result is presented in MATLAB/SIMULINK.

Configuration and Model Order Selection of Frequency-Dependent π Models for Representing DC Cables in Small-Signal Eigenvalue Analysis of HVDC Transmission Systems

Eigenvalue-based analysis of small-signal dynamics in high-voltage direct current (HVdc) transmission systems requires cable models that are compatible with a state-space representation. While distributed parameter models accounting for frequency-dependent effects are inherently incompatible with a state-space representation, a conventional $\pi $ model can only represent the cable behavior accurately at a single frequency. Instead, a frequency-dependent $\pi $ (FD- $\pi $ ) model consisting of a lumped circuit representation with multiple parallel $RL$ branches in each $\pi $ -section can be utilized to reproduce the frequency dependence of the cable characteristics in a specified frequency range. Based on an evaluation of relevant error metrics for FD- $\pi $ models, this article demonstrates how the number of sections and the number of parallel branches in each section will influence the accuracy. From this starting point, an optimization algorithm for identifying the configuration that fulfills a specified set of accuracy requirements with the lowest possible model order is introduced. A similar algorithm for identifying the most accurate FD- $\pi $ model within a specified maximum model order is also proposed. Examples of numerical results for different cable lengths and cross sections are presented to highlight their effect on the model, and it is demonstrated how the cable model configuration can influence the results from small-signal eigenvalue analysis of HVdc transmission systems.

Experimental study on the transformer effect in an ACSR cable

Steel-cored cables with an odd number of aluminum layers are affected by an electromagnetic phenomenon called transformer effect, due to the magnetization of the core. This phenomenon modifies the expected distribution of current density in the aluminum layers, affecting the alternating current (AC) resistance and resulting in having internal transient temperatures higher than at the cable outermost surface. Furthermore, the latter is the only variable monitored in terms of temperature, so being an utmost important phenomenon for the cable safe operation with high current capacity.This paper presents the results of a series of laboratory experiments on a three-layer ACSR “Duck” (54/7) cable. The current in each aluminum wire of the cable was measured simultaneously for different total current values and during the heating of the cable.Results show the distribution of current density between layers due to the transformer effect and a redistribution of current during the heating of the cable with the total current value being held constant. This redistribution can be attributed mainly to the presence of a radial difference of temperature between the steel core and the cable outer surface, which is expected at high current densities but has not been considered in previous theoretical studies. An example of calculating the current density distribution considering the radial temperature gradient is presented. The results highlight the importance of including the internal thermal behavior of steel-cored cables in the study of the transformer effect, especially on the perspective of increasing the current capacity of this type of cable.

Bifurcation and Chaotic Analysis for Cable Vibration of a Cable-Stayed Bridge

Cable-stayed bridges are of the most unique and cost-effective designs in modern bridge engineering. A key feature of these structures is that the cables or stays run directly from the tower to the deck. The nonlinear dynamic behavior of these cables can significantly affect the resilience and safety of the bridge. In this context, a deeper understanding of the bifurcation and chaotic mechanisms of cable vibration is highly desirable. Accordingly, in this study the nonlinear dynamic equation of a planar cable is derived for quantitative and qualitative analysis. The nonlinear system is solved asymptotically, using the conventional perturbation and two-timing scale methods, to study the periodic motion of the cables. The obtained solutions are primarily affected by the control parameters and the initial conditions. The asymptotic solutions are also simulated numerically. It is found that the chaotic behavior of cables is greatly affected by the governing parameters, including the cable dimensions, vibration amplitude, damping effect, and excitation frequency. Finally, seven state variables of the nonlinear system are analyzed to investigate the occurrence of bifurcation.