Cable Response Research Articles

Analytical solutions for resonant response of suspended cables subjected to external excitation

In this study, two analytical methods are applied to study the primary resonances response of suspended cables subjected to external excitation. We choose four different sag-to-span ratios and the first two modes to investigate the differences in nonlinear responses obtained with analytical methods. First, we summarize the equations of motion by applying the Hamilton’s principle and quasi-static assumption, and then these equations are discretized by the Galerkin procedure. Second, the multiple-scale method and homotopy analysis method are adopted to obtain the approximate solutions. Moreover, numerical integrations are introduced in order to verify the obtained approximate results. The numerical results show that frequency response curves obtained by different analytical methods show different quantitative predictions in some cases of motion, modes, and particular sag-to-span ratios. Finally, the differences in displacement fields and axial tension forces are compared and analyzed.

A two-degree-of-freedom aeroelastic model for the vibration of dry cylindrical body along unsteady air flow and its application to aerodynamic response of dry inclined cables

A two-degree-of-freedom aeroelastic model is proposed to study wind-induced response of bridge stay cables in the context of a rigid circular cylinder model oscillating in an arbitrary orientation with respect to the oncoming unsteady flow. Compared to the existing analytical models and wind tunnel studies, the proposed model can take into account the unsteady characteristics of natural wind and predict the evolving history of cable response. The validity of the proposed model is verified by the results from an earlier wind tunnel study. The rationality of defining a cable aerodynamic stability criterion using solely the Ur–Sc relation is discussed. Two different unsteady wind models are used to investigate the impact of flow unsteadiness on the wind-induced response of stay cables. A case study is presented to evaluate the aerodynamic behavior of a real bridge stay cable in unsteady/turbulent natural wind. Results show that while the emergence of critical Reynolds number regime is crucial for the onset of dry inclined cable galloping, the spanwise correlation of aerodynamic forces acting on a cable and the sustained duration of critical flow condition are the determining factors for the continuous growth of unstable cable response and the eventual occurrence of this type of aerodynamic instability.

Bakeout Effects on Dynamic Response of Spaceflight Cables

Spaceflight cables are investigated to determine the effect of bakeout on their dynamic response, including resonant frequencies and damping ratios. The addition of cable harnesses to spacecraft structures can affect the dynamic response of the entire structure, especially for lightweight structures with high cable mass ratios. Bakeout, a heat and vacuum treatment that spaceflight components must undergo, may change the dynamic stiffness of flight cables and thus the dynamics of the cabled host structure. Bakeout effects are examined by experimentally identifying natural frequencies and damping values for spaceflight cables before and after the bakeout process. After bakeout, the first natural frequency decreases by an average of 14% for all single-strand cables and by 24% for multistrand cables. The second natural frequency decreases by 8 to 17% for all cables. Bakeout also increases the damping percentage for single and multistrand cables. These results show that bakeout affects the dynamic response of spaceflight cables significantly and should be taken into account when using cable data for design purposes.

Alternation of Flex Cable Vibration Modes in High Precision Hard Disk Drives

For fast and accurate data accessing operations, flex cable's vibratory response has been identified to be the key development focus for magnetic hard disk drives to meet near nanometer precision accuracy. Dampening the cable's dynamics with damper layers and revising the seek servo designs have been the common approaches found in the literature to reach the requirement. In this paper, vibrations of nonuniform flex cable, which is composed of baseline flex cable layers and addition of piezoelectric layer such as polyvinylidene fluoride film, are investigated through experiments and non-classical, reduced-order finite element analysis. It is found that the addition of the piezofilm changes the cable's natural frequencies only within 3% error range but alters the cable's bending vibration mode shapes significantly. The change in the cable's mode shapes leads to change of the known cable/actuator dynamic coupling reported in the literature. Results presented in this paper establish mechanical framework for active control of the flex cable onto the rotary actuator.

Effects of cables damage on vertical and torsional eigenproperties of suspension bridges

This paper presents a continuum model for the nonlinear coupled vertical and torsional vibrations of suspension bridges with arbitrary damage in one main cable and, after pursuing a suitable linearization of the equations of motion, an investigation of damage effects on modal parameters. Damage is modeled as a diffused loss of cross-section representing the typical effect of fretting fatigue and it is introduced in the formulation by enforcing relevant literature results providing analytical solution for the static response of damaged suspended cables. The coupled nonlinear equations of motion of the damaged bridge, including the effects of shear deformation, rotary inertia and warping of the cross-section of the girder, are derived by application of Hamilton׳s principle. In this way, the equations of motion available in the literature for undamaged suspension bridges are generalized to the presence of arbitrary damage in one main cable and the resulting eigenfrequencies and eigenfunctions are derived in an analytical fashion. An extensive parametric investigation is finally presented to discuss damage effects on eigenfunctions and eigenfrequencies under variation of practically meaningful parameters.

2D numerical analysis on evolution of water film and cable vibration response subject to wind and rain

Under wind and rain, cables of cable-stayed bridges may vibrate with large amplitude known as rain–wind induced vibration (RWIV). According to the previous researches, the formation and oscillation of water rivulets around cable plays an important role in RWIV. In this paper, 2D coupled equations of water film evolution and cable vibration are presented for the first time based on the combination of lubrication theory and vibration theory of single-mode system. To reveal the mechanism of RWIV, the mutual influences of water film evolution, lift and vibration of cable under different wind speeds are analysed by numerically solving the coupled equations. In accordance with the experimental results, the numerical results show that RWIV only occurs in special wind speed and the period of water film evolution is close to cable natural period, which makes cable vibrate with large amplitude. Under too low wind speed, the inconspicuous variation of water film morphology leads to small amplitude of lift and cable vibrating like free vibration. And when wind speed is too large, cable also vibrates with small amplitude as the water film morphology and lift change with little periodicity. These confirm the conclusion that the resonance between rivulets and cable may be one of the main reasons for RWIV.

Assessment of Improved Power Quality Due to Fault Current Limiting HTS Cable

Fault current limiting high-temperature superconductor (FCL-HTS) cable not only provides effective power transmission, but also reduces the negative impact of fault current. As the demand grows rapidly, distributed generation (DG) is being implemented into the power grids. The integration of DG into the existing power grid causes an increase in short circuit current. In order to facilitate reliable planning and operation of future power systems, power system planners and operators will need to avoid the potential threat of increased fault current. The superconductor cable is considered as an enabling technology because it can raise power transmission capability and effectiveness with minimal loss. However, high fault current through the superconductor cable may seriously damage the power system. However, FCL-HTS cables can reduce the impact from unexpected high fault current. The FCL-HTS cable helps avoid interruption and voltage sag without harming existing coordination of protection devices. This study addresses the power quality issues for increased fault current that will be caused by the DG. We also analyze the response of FCL-HTS cable in perspective of power quality, when the fault occurs with DG.

Vision-Assisted Vibration Analysis of Inhomogeneous Flexible Cables in Hard Disk Drives

Reduction of flexible cable vibrations has been one of the key engineering focuses for magnetic disk drives to meet subnanometer recording precision requirement. Common approach to reduce the vibrations is to adopt additional polyimide-like damping layer on underlying homogeneous flexible cable, adding in homogeneity long the cable's dynamic loop. This paper investigates the effect of inhomogeneous composition along the cable's dynamic loop on the cable's vibration modes. The cable's profiles are obtained by experimental image processing and used in the proposed finite element model. It is found that placement and design of the inhomogeneous composition such as the damping layer for passive vibration control or piezoelectric layer for active vibration control can significantly alter the cable's modal responses, which potentially can be used to reduce transmission of the cable's vibrations onto the rotary actuator.

Switching Sampling Power Meter for Frequencies Up to 1 MHz

This paper describes a power measurement setup that is able to measure power up to the MHz region. The setup consists of a commercial digitizer together with a switch unit, and buffer amplifiers to alternately measure the voltage and current channel. A reference AC voltmeter provides an absolute reference by simultaneous measurement of the rms voltage of one channel, which significantly reduces the need for flat frequency response of the setup. The method described in this paper makes complex voltage ratio measurements possible in the range of 50 Hz up to 1 MHz with an uncertainty of a few parts in $10^{6}$ and in addition can be applied in wideband power measurements. Using our new method, the frequency response of cables and several other components is no longer a limiting factor for power measurements up to 1 MHz.

Dynamic performance of a cable with an inspection robot — analysis, simulation, and experiments

A special cable inspection robot is designed to inspect automatically the cables of a cable-stayed bridge. The free vibration equation of the cable-robot system is derived firstly to study the dynamic characteristics and safety performance of the system. Then, the effect of the robot on the cable natural frequency is discussed, and the dynamic response equation when a robot is climbing at a constant speed is deduced. Furthermore, the effect of the cable vibration on the robot’s climbing ability is studied. The natural frequency characteristics of the robot are analyzed and optimized to avoid the resonance between the cable and the robot, using a finite element model. Additionally, dynamic cable responses are simulated under different conditions wherein the robot mass are 10 and 200 kg, and the speeds are 0.2 and 0.3 m/s, respectively. At last, to demonstrate further the dynamic characteristics of the cable-robot system experimentally, cables are set up on the Junshan highway bridge over the Yangtze river. Similar experimental models of these cables are constructed, and vibration experiments are conducted to validate the theoretical calculation. The results show that a light robot has little effects on the cable vibration amplitude and vibration acceleration; this confirms the safety of the cable.

Superelastic shape memory alloy cables: Part II – Subcomponent isothermal responses

This paper constitutes the second part of our experimental study of the thermo-mechanical behavior of superelastic NiTi shape memory alloy cables. Part I introduced the fundamental, room temperature, tensile responses of two cable designs (7×7 right regular lay, and 1×27 alternating lay). In Part II, each cable behavior is studied further by breaking down the response into the contributions of its hierarchical subcomponents. Selected wire strands were extracted from the two cable constructions, and their quasi-static tension responses were measured using the same experimental setup of Part I. Consistent with the shallow wire helix angles in the 7×7 construction, the force–elongation responses of the core wire, 1×7 core strand and full 7×7 cable were similar on a normalized basis, with only a slight decrease in transformation force plateaus and slight increase in plateau strains in this specimen sequence. By contrast, each successive 1×27 component (1×6 core strand, 1×15 strand, and full cable) included an additional outer layer of wires with a larger number of wires, greater helix radius, and deeper helix angle, so the normalized axial load responses became significantly more compliant. Each specimen in the sequence also exhibited progressively larger strains at failure, reaching 40% strain in the full 1×27 cable.Stress-induced phase transformations involved localized strain/temperature and front propagation in all of the tested 7×7 components but none of the 1×27 components aside from the 1×27 core wire. Stereo digital image correlation measurements revealed finer features within a global transformation front of the 1×7 core strand than the 7×7 cable, consisting of an staggered pattern of individual wire fronts that moved in lock-step during elongation. Although the 1×27 multi-layer strands exhibited temperature/strain localizations in a distributed pattern during transformations, the localizations did not propagate and their cause was traced back to contact indentations (stress concentrations) arising from the cable’s fabrication. The normalized axial torque responses of the multi-layer 1×27 components during transformation were distinctly non-monotonic and complex, due to the alternating handedness of the layers. Force and torque contributions of individual wire layers were deduced by subtracting 1×27 component responses, which helped to clarify the transformation kinetics within each layer and explain the unusual force and torque undulations seen in the 1×27 cable response of Part I.

A linear model of stationary elevator traveling and compensation cables

Based on a recent asymptotic analysis of a nonlinear model of a slack cable, a computationally efficient, linear model is developed for calculating the natural frequencies, mode shapes, and dynamic responses of stationary elevator traveling and compensation cables. The linear cable model consists of two vertical cable segments connected by a half-circular lower loop. The two vertical cable segments are modeled as a string with a variable tension due to the weight of the cable. The horizontal displacements of the cable segments consist of boundary-induced displacements and relative elastic displacements, where the boundary-induced displacements are interpolated from the displacements of the two lower ends of the cable segments, and the relative elastic displacements satisfy the corresponding homogeneous boundary conditions of the cable segments. The horizontal displacement of the lower loop is interpolated from those of the two lower ends of the two cable segments, and the bending stiffness of the lower loop is modeled by a spring with a constant stiffness, which can be calculated from the nonlinear model. Given a car position, the natural frequencies and mode shapes of an elevator traveling or compensation cable are calculated using the linear model and compared with those from the nonlinear model. The calculated natural frequencies are also compared with those from a full-scale experiment. In addition, the dynamic responses of a cable under a boundary excitation are calculated and compared with those from the nonlinear model. There is a good agreement between the predictions from the linear and nonlinear models and between the measured natural frequencies from the full-scale experiment and the corresponding calculated ones.

Nonlinear in-plane vibrations of inclined cables carrying moving oscillators

In-plane dynamics of small-sag inclined cables carrying a stream of oscillators moving with arbitrarily varying velocity is addressed. A condensed model of the coupled cable-moving oscillators system is derived by referring cable vibrations to a local Cartesian coordinate system. Specifically, relying on the negligible influence of the inertia forces along the cable chord and assuming a quasi-static stretching during the motion, an appropriate static condensation procedure is applied which enables to account for the chordwise components of the interaction forces between the cable and the moving sub-systems . Thus, the governing equations are reduced to a unique nonlinear integro-differential equation in the transverse displacement of the cable coupled to the ordinary differential equations ruling the response of the moving oscillators in terms of absolute displacements. The condensed model is discretized by the Galerkin method assuming an improved series expansion of cable response able to accurately reproduce the abrupt changes of cable profile at the contact points with the moving oscillators.A numerical application is presented to validate the proposed condensed model of the inclined cable under moving oscillators as well as the improved series representation of cable response.

Wind-induced response and excitation characteristics of an inclined cable model in the critical Reynolds number range

This paper focuses on wind-induced vibrations of dry inclined bridge cables in the critical Reynolds number range. The cable response and the associated wind load characteristics are studied experimentally, in the third phase of a major wind tunnel investigation on cable aerodynamics at the National Research Council Canada. The displacement (and acceleration) response of a 6.7m long section cable model, 160mm in diameter, was monitored simultaneously with 162 surface pressure taps, for inclinations of 60°, 77° and 90°. The data corroborate the susceptibility of dry cables to respond, primarily in the across-flow direction, to load variations associated with transitions between flow regimes throughout the drag crisis region. The most vigorous vibrations (stopped at approximately 60% diameter response amplitude) were observed at 60°, with damping ratios below 0.2%. Significant “lock-in” between the lift force and the violent sway cable response was identified in terms of the transfer function between the two during the large vibration events. The large responses were confined to a narrow Reynolds number range, often at flow conditions giving the minimum normal (drag) coefficient and a significant derivative of the lift coefficient with respect to Reynolds number. Throughout the drag crisis region, significant variation in flow characteristics along the cable aligned at 60° has been observed, in terms of both mean pressure distributions and pressure fluctuations.

Dynamic Response of the Stay Cable under Bridge Deck Excitation

Modeling the dynamic response of the stay cable under bridge deck excitation represents a complex task for cable design procedure and forms an important step in the cable mitigation design. This paper analyses the characteristics of cable response under bridge deck excitation. The problem of cable vibration under the harmonic oscillation of the supports is considered as the external excitation. The formulae for the estimation of maximum amplitude of cable vibration are presented to determine the main cause of large amplitude vibration of the cable under indirect excitation.

Numerical simulation of cables in widespread use in the nuclear power industry subjected to fire

Numerical simulation is used to increase the knowledge base for failure of instrumentation or control cables utilized in the nuclear power industry subjected to an industrial fire. The model used for the simulation includes the electrical core of the conductors, the enveloping insulation, the filler material, and the jacket. All told, 22 cables in present use in the nuclear industry are investigated. The focus of the work is to determine the time at which a cable ceases to perform. That time is based on a definition provided by NUREG/CR-6931: Cable Response to Live Fire. It was found that the time to failure is well correlated with the thermal mass per unit length of the cable. The correlating equation, useful for interpolation is, Time to failure=(1376) (total thermal mass per unit length)+111. In this equation, the time to failure is in seconds, and the thermal mass per unit length, defined in Eq. (4), has units of kilojoules per degree Kelvin per meter. When comparing the numerical simulation to experimentation reported in NUREG/CR-6931: Cable Response to Live Fire, the correlation was found to be a conservative estimate of the time to failure.

Heated Distributed Temperature Sensing for Field Scale Soil Moisture Monitoring

Characterizing both spatial and temporal soil moisture (θ) dynamics at site scales is difficult with existing technologies. To address this shortcoming, we developed a distributed soil moisture sensing system that employs a distributed temperature sensing system to monitor thermal response at 2 m intervals along the length of a buried cable which is subjected to heat pulses. The cable temperature response to heating, which is strongly dependent on soil moisture, was empirically related to colocated, dielectric-based θ measurements at three locations. Spatially distributed, and temporally continuous estimates of θ were obtained in dry conditions (θ≤ 0.31) using this technology (root mean square error [RMSE] = 0.016), but insensitivity of the instrument response curve adversely affected accuracy under wet conditions (RMSE = 0.050).

A nonlinear frequency analysis based approach for power cable insulation fault detection

PurposeThe present study is concerned with the application of a nonlinear frequency analysis approach to the detection and location of water tree degradation of power cable XLPE insulation without turning off electric power.Design/methodology/approachThe use of power cable system responses to power line carrier signals are proposed to conduct the required signal analysis for damage location purpose. This technique is based on the fact that the water tree degradation in power cables can make the system behave nonlinearly. Consequently, the location of water tree degradation can be determined by detecting the position of nonlinear components in power cable systems.FindingsA novel method has been proposed for locating water tree degradation in power cable systems; numerical simulation studies have demonstrated the effectiveness of the new technique.Originality/valueThe proposed technique has the potential to be applied in practice to more effectively resolve the power cable damage location problem.

The Study of Super Element Cable

A parametric super element model for cable passing through multiple pulleys is presented in this study for the static analysis of structures.Crossing cable, with varying wind velocity, have shown the expression for in-plane cable vibrations to give good estimates of the actual aerodynamic damping.The load can be adjusted from 20% to 100% of the power supplied and the number of branches connected can be altered. The discretization is carried out by a standard approach and the resulting model is presented adopting a compact vectorial formalism enabling the formulation of expressions. Generation of closely spaced modes due to the addition of the secondary cable plays an important role on its controlling effects on the main cable response through this type of nonlinear interaction.

Static and dynamic response of elastic suspended cables with thermal effects

Cable structures are often subjected to severe and variable environmental conditions, and their mechanical behavior is known to be particularly sensitive to different ambient factors. The paper analyzes temperature effects on the static and dynamic response of suspended inclined cables through a continuous monodimensional model including geometric nonlinearities. Uniform temperature changes are introduced through a non-homogeneous constitutive law for the material linear elasticity. Exact and approximate solutions of the equations governing the cable static equilibrium under self-weight are achieved, and the significance of the temperature-dependent variation of tension and sag are parametrically investigated. The spectral properties characterizing the free dynamics are obtained in a closed-form fashion for shallow parabolic cables within the low frequency vibration range. The sensitivity of the linear frequencies to temperature changes is discussed, outlining two thermal effects, which are distinguished by their different origins, geometric or static. For a generic temperature change, the geometric effect produces a systematic increment or reduction of all the frequencies, for both symmetric and anti-symmetric modes. The static effect stiffens or softens only the symmetric modes, and may prevail over the competing geometric effect, depending on the cable Irvine parameter. Finally, the thermal effects on the frequency veering and modal hybridization phenomena, which characterize quasi-resonant shallow cubic cables, are analyzed.