Cable Response Research Articles

Influence of Negative Phase Loading on Cable Net Facade Response

AbstractThe behavior of cable net facades subjected to blast loads differs significantly from the behavior of stiffer structures, such as post-and-rail facades or classical concrete or steel structures. The low eigenfrequencies and the relatively small specific weight of cable net facades cause larger deformations and higher structural velocities. The negative pressure phase of a blast load can especially have a significant effect on the structural response. The negative phase can either increase or decrease the deflections. Nevertheless, the United States and international threat levels according to the United States General Services Administration and the ISO neglect the negative phase of blast loads. In the present investigation, a comparison and assessment was done to present the differences between the standard blast load model, that is, a triangular-shaped blast load neglecting the negative phase, and the exponentially decaying Friedlander blast load model, which takes the negative phase into accoun...

A Force Method Model for Static Analysis of Transmission Line System Subjected to in-Plane and Out-of-Plane Loadings

In this paper, transmission line systems are modeled as multi-span cable structures. A force method model is proposed for analysing the static response of the multi-span cables with small sags. The accepted cable model reduces to two groups of differential equations (the equilibrium equations in y, z directions) and an integral equation (the compatibility equation). Substituting the differential equation solutions into the compatibility condition, the governing equation is obtained in terms of the tension component in chord direction. This equation has been named the force method equation (FME). In this way the infinite-degree-of-freedom dynamic system is effectively simplified to a system with only one unknown. Finally, one example is presented to illustrate the application of the proposed force method.

Application of Chebyshev Series to Solution of Cable Vibration Problems

In order to obtain simple formulae of cable dynamic behavior for numerical computation, the Chebyshev series method for the free vibration analysis of a cable considering boundary condition and flexural stiffness is utilized. The differential eigenvalue problem is reduced to an algebraic system which gives approximate eigenfrequencies and mode shape functions for a cable. These simple and approximate formulae are of value in the analysis of cable dynamic response and may be proved useful in the design of cable structures. The proposed approach is applicable to a wide range of cables.

Bifurcation analysis of a parametrically excited inclined cable close to two-to-one internal resonance

This paper presents a study of how different vibration modes contribute to the dynamics of an inclined cable that is parametrically excited close to a 2:1 internal resonance. The behaviour of inclined cables is important for design and analysis of cable-stayed bridges. In this work the cable vibrations are modelled by a four-mode model. This type of model has been used previously to study the onset of cable sway motion caused by internal resonances which occur due to the nonlinear modal coupling terms. A bifurcation study is carried out with numerical continuation techniques applied to the scaled and averaged modal equations. As part of this analysis, the amplitudes of the cable vibration response to support inputs is computed. These theoretical results are compared with experimental measurements taken from a 5.4 m long inclined cable with a vertical support input at the lower end. In general this comparison shows a very high level of agreement.

Prediction of unwinding behaviors and problems of cables from inner-winding spool dispensers

Wire-guided control technologies are widely used to increase the targeting accuracy of advanced military weapons through the use of unwinding dispensers to guarantee that unwinding occurs without any problems, such as tangling or cutting. In this study, the transient behaviors of cables unwinding from inner-winding cylindrical spool dispensers are investigated. The cable is withdrawn from the spool dispenser at a constant velocity through a fixed point located along the axis of the spool dispenser. And when the cable is flown out of the dispenser, because several dynamic forces such as inertial forces, Coriolis forces, centrifugal forces, tensile forces, and fluid-resistance forces act on the cables, the cables exhibit highly nonlinear and complex unwinding behaviors which are called as unwinding balloons. For predicting these complex unwinding motions, the governing equations of motion for cables unwinding from a cylindrical spool dispenser of the inner-winding type are derived using the extended Hamilton’s principles for an open system in which mass can be transported at each boundary. Modified finite difference methods are used to discretize the spatial variables of the derived nonlinear partial differential equations. The time responses of the unwinding cables are calculated using Newmark time integration methods. Finally, in order to present numerical examples, an inner-winding spool dispenser that can be unwound up to a length of 50 km is designed by using simple geometrical relationships. The behaviors during unwinding from the designed inner spool dispenser are presented and modifications of the spool dispenser for avoiding unwinding problems are proposed by using the suggested numerical methods.

VIBRATION CONTROL OF DIFFERENT FRP CABLES IN LONG-SPAN CABLE-STAYED BRIDGE UNDER INDIRECT EXCITATIONS

To identify the vibration characteristics and potential vibration control of different fiber reinforced polymer (FRP) cables for long-span cable-stayed bridges, the critical resonant responses of these cables under indirect excitations including external and parametric excitations are studied in this paper. Based on theoretical equations, the primary resonant responses of different cables under indirect excitations were first calculated and compared, afterwards the influence of cable length and design stress to the resonant responses and the importance of external and parametric excitations were further studied. Analysis of results show that all of the FRP cables measuring 575 m in length possess lower resonant responses compared with steel cables, while the hybrid FRP cable with smart dampers exhibits even lower responses than the other FRP cables. Moreover, the external excitation induced resonance will become critical for some kinds of FRP cables with increasing cable length. A method on adjusting design stresses mitigates this critical resonance and benefits vibration control of FRP cables. In addition, parametric excitation plays a more important role in resonant responses for short-length cables in comparison to external excitation, whereas both parametric and external excitations are critically important for long-length cables.

Derivation of equations of motion of an unwinding cable from a cylindrical spool package

In this study, the transient analysis of a cable unwinding from a cylindrical spool package is studied. Cables are withdrawn with a constant velocity through a fixed point which is located along the axis of the package. When the cable is flown out of the package, several dynamic forces, such as inertial force, Coriolis force, centrifugal force, tensile force, and fluid-resistance force are acting on the cable. Consequently, the cable becomes to undergo very nonlinear and complex unwinding behavior which is called unwinding balloon. In this paper, to prevent the problems during unwinding such as tangling or cutting, unwinding behaviors of cables in transient state were derived and analyzed. First of all, the governing equations of motion of cables unwinding from a cylindrical spool package were systematically derived using the extended Hamilton’s principles of an open system in which mass is transported at each boundary. And the modified finite difference methods are suggested to solve the derived nonlinear partial differential equations. Time responses of unwinding cables are calculated using Newmark time integration methods.

Parametric vibration of carbon fiber reinforced plastic cables with damping effects in long-span cable-stayed bridges

Carbon fiber reinforced plastic (CFRP) cables are superior to steel cables in cable-stayed bridges due to their light weight and excellent durability. It is a kind of flexible structural component with strongly weak shear stiffness. Hence, understanding the dynamic properties of CFRP cables poses a significant issue in bridge engineering. In this paper, the parametric vibrations of CFRP cables is performed and compared with steel cables by using a non-linear finite element method. The CFRP and steel cables of a cable-stayed bridge with a span of 1400 m, designed by the same criteria, are studied as typical cases. The material damping, aerodynamic damping and viscous dampers are simulated in the analysis, and the variations of the material damping and aerodynamic damping due to amplitude variations are taken into consideration. The dynamic responses of cables due to stochastic and harmonic support excitations are investigated. Numerical results show that the vibration amplitudes of steel cables are greater than that of CFRP cables. The parametric vibration of CFRP cable is more sensitive to damping than that of steel cable. The effects of material damping and viscous dampers on parametric vibration of both steel and CFRP cables are very significant, while that of aerodynamic damping is inferior to the former two dampers.

Finite Difference Thermoelastic Analysis of Suspended Cables Including Extensibility and Large Sag Effects

This paper presents and validates an original and practical finite difference model to investigate the thermoelastic response of suspended cables. The mathematical formulations are provided for various loading cases. The model includes the effects of cable extensibility and large sag, as well as variability of temperature gradients and thermal properties of the cable along its arc-length. The formulations are programmed and used to study suspended cables subjected to different thermomechanical loads. The results are validated against analytical or finite element solutions, and the proposed model is shown accurate and efficient in assessing the thermoelastic response of suspended cables.

Performance evaluation of shape-memory-alloy superelastic behavior to control a stay cable in cable-stayed bridges

This paper focuses on introducing and investigating the performance of a new passive control device for stay cable in cable-stayed bridges made with shape-memory alloys (SMA). The superelasticity and damping capability of SMA is sought in this study to develop a supplementary energy dissipation device for stay cable. A linear model of a sag cable and a one-dimensional constitutive model for the SMA are used. The problem of the optimal design of the device is studied. In the optimization problem, an energy criterion associated with the concept of optimal performance of the hysteretic connection is used. The maximum dissipation energy depends on the cross-sectional area, the length, and the location of the SMA on the cable. The effectiveness of the SMA damper in controlling the cable displacement is assessed. Furthermore, a study is conducted to determine the sensitivity of the cable response to the properties of the SMA device. The comparison between the SMA damper and a more classical passive control energy dissipation device, i.e., the tuned mass damper (TMD), is carried out. The numerical results show the effectiveness of the SMA damper to damp the high free vibration and the harmonic vibration better than an optimal TMD.

Design of wireless sensor network and its application for structural health monitoring of cable-stayed bridge

A low-cost wireless sensor network (WSN) solution with highly expandable super and simple nodes was developed. The super node was designed as a sensing unit as well as a receiving terminal with low energy consumption. The simple node was designed to serve as a cheaper alternative for large-scale deployment. A 12-bit ADC inputs and DAC outputs were reserved for sensor boards to ease the sensing integration. Vibration and thermal field tests of the Chi-Lu Bridge were conducted to evaluate the WSN's performance. Integral acceleration, temperature and tilt sensing modules were constructed to simplify the task of long-term environmental monitoring on this bridge, while a star topology was used to avoid collisions and reduce power consumption. We showed that, given sufficient power and additional power amplifier, the WSN can successfully be active for more than 7 days and satisfy the half bridge 120-meter transmission requirement. The time and frequency responses of cables shocked by external force and temperature variations around cables in one day were recorded and analyzed. Finally, guidelines on power characterization of the WSN platform and selection of acceleration sensors for structural health monitoring applications were given.

Stochastic and chaotic sub- and superharmonic response of shallow cables due to chord elongations

The paper deals with the non-linear response of shallow cables driven by stochastically varying chord elongations caused by random vibrations of the supported structure. The chord elongation introduces parametric excitation in the linear stiffness terms of the modal coordinate equations, which are responsible for significant internal subharmonic and superharmonic resonances. Under harmonically varying support motions coupled ordered or chaotic in-plane and out-of-plane subharmonic and superharmonic periodic motions may take place. If the harmonically varying chord elongation is replaced by a zero-mean, stationary narrow-band random excitation with the same standard deviation and center frequency, qualitatively and quantitatively completely different modes of vibration are registered no matter how small the bandwidth of the excitation process is. Additionally, the stochastic excitation process tends to enhance chaotic behavior. Based on Monte Carlo simulation on a reduced non-linear two-degree-of freedom system the indicated effects have been investigated for stochastic subharmonic resonance of order 2:1, and stochastic superharmonic resonances of orders 1:2 and 2:3. By analyzing the responses for two chord elongation processes with almost identical auto-spectral density function, but completely different amplitudes, it is shown that the indicated qualitative and quantitative changes of the subharmonic resonance primarily are caused by the slowly varying phase of the stochastic excitation. The superharmonic stochastic responses are dominated by random jumps between a single mode in-plane and a coupled mode attractor, which are caused by the variation of the amplitude of the random excitation. Such jumps do not occur in the subharmonic response, because the single mode in-plane attractor is unstable.

Stochastic Response of an Inclined Shallow Cable with Linear Viscous Dampers under Stochastic Excitation

Considering the coupling between the in-plane and out-of-plane vibration, the stochastic response of an inclined shallow cable with linear viscous dampers subjected to Gaussian white noise excitation is investigated in this paper. Selecting the static deflection shape due to a concentrated force at the dampers location and the first sine term as shape functions, a reduced four-degree-of-freedom system of nonlinear stochastic ordinary differential equations are derived to describe dynamic response of the cable. Since only polynomial-type terms are contained, the fourth-order cumulant-neglect closure together with the C-type Gram-Charlier expansion with a fourth-order closure are applied to obtain statistical moments, power spectral density and probabilistic density function of the cable response, whose availability is verified by Monte Carlo method. Taking a typical cable as an example, the influence of several factors, which include excitation level and direction as well as damper size, on the dynamic response of the cable is extensively investigated. It is found that the sum of mean square in-plane and out-of-plane displacement is primarily independent of the load direction when the excitation level and viscous coefficient of the damper are fixed. Moreover, the peak frequency and half-band width of the spectra of both the in-plane and the out-of-plane displacements are increasing with excitation level when the damper size is constant. It is also observed that, even though the actual optimal damper size is slightly greater than the one obtained by the complex modal theory, the difference of statistical moment of the cable caused by these two damper size is negligible, so the vibration reduction effect provided by the theoretical optimal viscous coefficient is satisfactory.

Three-dimensional imaging of electrical conductivity in the mantle transition zone beneath the North Pacific Ocean by a semi-global induction study

The three-dimensional (3-D) electrical conductivity distribution in and around the mantle transition zone (MTZ) beneath the north Pacific is imaged by inverting revised geomagnetic responses at 13 geomagnetic observatories and cable responses of 8 long baseline submarine cables in the area. Two one-dimensional (1-D) models representing the average structure beneath the north Pacific were employed as the reference and initial models for the 3-D conductivity inversions. The features in the revised semi-global conductivity model in the MTZ are (1) a high conductivity anomaly beneath the Philippine Sea, (2) a high conductivity anomaly beneath the Hawaiian Islands, and (3) a low conductivity anomaly beneath and in the vicinity of northern Japan. Arrhenius plots of the conductivity and temperature estimated from global seismic tomography models indicate that the anomalies in the MTZ beneath northern Japan and most areas under Hawaii can be explained mainly by the temperature effect, but that the conductivity beneath the Philippine Sea requires an additional cause to explain the higher conductivity. If the cause is the effect of water, then the present result suggests high water content of 1wt% or more throughout the MTZ beneath the Philippine Sea.

TRANSIENT RESPONSES OF COAXIAL CABLES IN AN ELECTRICALLY LARGE CABIN WITH SLOTS AND WINDOWS ILLUMINATED BY AN ELECTROMAGNETIC PULSE

An improved flnite-difierence time-domain (FDTD) method is proposed for predicting transient responses of coaxial cables which are placed in an electrically large metallic cabin with arbitrary slots and circular windows on its wall. By integrating nodal analysis, multi-conductor transmission line (MTL) equation and FDTD method, we are able to accurately capture electromagnetic interference (EMI) efiects on the cables. Our developed algorithm is verifled by calculat- ing frequency-dependent transfer impedance of coaxial cables together with induced currents. Numerical calculations are further performed to show the near-end coupled current responses of braided and tubular cables, respectively, and the efiects of incident directions and polar- izations of the illuminated electromagnetic pulse are both taken into account.

Controlling parameter for wave types of long flexible cable undergoing vortex-induced vibration

Submerged floating tunnel (SFT) is a popular concept of crossing waterways. The failure of the cable may occur due to vortexinduced-vibration (VIV), and the stability of the cable is crucial to the safety of the entire tunnel. Investigation results in recent years show that the vortex-induced vibration of the flexible cables with large aspect ratio reveals some new phenomena, for example, the vortex-induced wave, multi-mode competition, wide band random vibration, which have brought new challenges to the study of vortex-induced vibration of long flexible cables. In this paper, the dimensionless parameter controlling the wave types of dynamic response of slender cables undergoing vortex-induced vibration is investigated by means of dimensional analysis and finite element numerical simulations. Our results indicate that there are three types of response for a slender cable, i.e. standing wave vibration, traveling wave vibration and intermediate state. Based on dimensional analysis the controlling parameter is found to be related to the system damping including fluid damping and structural damping, order number of the locked-in modes and the aspect ratio of cable. Furthermore through numerical simulations and parameter regression, the expression and the critical value of controlling parameter is presented. At last the physical meaning of the parameter is analyzed and discussed.

A Closed-Form Refined Model of the Cables' Nonlinear Response in Cable-Stayed Structures

In this paper a refined second-order model for the analysis of the elastic response of cables in cable-stayed structures is proposed. Starting from the exact catenary theory, the Dischinger-Ernst formulation is rationally deduced and, performing a second order approximation both with respect to the stress variation and the apparent chord-strain one, a refined explicit equivalent constitutive relationship for elastic stays is obtained. Moreover, the geometrical non-linearities induced on the cable by the deformation of the stay-supported structure are taken into account through a second order displacement approach. Accordingly, a closed-form formulation describing nonlinear cable-structure interaction effects is obtained which, unlike the classical secant model, does not need iterative procedures, opening the possibility to develop refined analytical solutions for cable structures. Several numerical examples and benchmarks on different stay configurations are presented, showing the effectiveness and the accuracy of the proposed model.

Cooling Configuration Design Considerations for Long-Length HTS Cables

Recent successes in demonstrating high temperature superconducting (HTS) cable systems hundreds of meters in length have inspired even longer length projects. A compact and energy efficient cooling configuration can be achieved using a counterflow-cooling arrangement. This is particularly attractive when all three phases are contained in a single cryostat because of the elimination of the space and thermal requirements of a separate liquid nitrogen return line. Future cable projects will utilize second generation (2G) wire which is expected to become lower in cost but may have different thermal requirements than first generation (1G) BSCCO wire due to the lower critical temperature and to a lesser extent, the lower thermal conductivity of the wire. HTS cable configurations are studied with a numerical model to assess thermal hydraulic performance with AC and thermal losses; a summary of the results from the analysis will be presented. An analysis of the cable thermal-hydraulic response to over-current faults will be presented.

Optimal Design of Shape Memory Alloy Damper for Cable Vibration Control

In order to apply shape memory alloy (SMA) damper for effective control of cable vibration under external excitations, motion equations and corresponding state equation of the system made up of SMA dampers and a cable are described based on Hamilton Principle, and the system's optimization problems based on the linear quadratic regulator (LQR) active control algorithm are investigated to obtain the optimum cable vibration control effects and control forces. According to the equivalency between SMA damper optimum passive control effects and LQR active control effects, the optimal design principle and methods of SMA damper for cable vibration control are proposed. Utilizing the above optimal methods, a SMA damper is designed to control vibration of a practical cable under white noise excitations, and its control effects are compared with the LQR active control effects by numerical simulation. Results show that the cable vibration responses under both LQR active control and SMA damper optimum control are obviously less than those without control, and SMA damper optimum control effects are approached to the LQR active control effects. This may indicate the effectiveness of the supposed SMA damper optimum design methods for cable vibration control.

Damage Identification in Elastic Suspended Cables through Frequency Measurement

Structural cables in cable-stayed systems are subject to potential damage, mainly due to fatigue phenomena and galvanic corrosion. The paper analyzes how the dynamical behavior of cables is affected by diffuse damage, and investigates whether the damage can be identified through information selected from the dynamical response. A continuous monodimensional model of a damaged cable is used for this purpose. Damage is described as a reduction of the cable cross section, and defined in terms of its intensity, extent and position. The major effects of these different damage parameters on the cable static response and spectral properties are evidenced and discussed to verify the observability of the damage. The frequencies of the dominant transversal motion of the cable are chosen as damage indicators, since they are sufficiently sensitive to the damage intensity and extent, while the damage position requires additional information. The damage identification problem is formulated by defining an objective error function between the measured and the model frequencies, to be minimized in the space of the damage parameters. Pseudo-experimental data are initially used to test the effectiveness and resolution of the procedure. The results confirm the uniqueness of the problem solution and its correctness. The robustness of the solution is discussed while considering the presence of random errors of increasing amplitude. The procedure is also positively verified with experimental measures from a prototype model of an artificially damaged spiral strand.