• Title, Summary, Keyword: cable stiffness

### Stochastic stability control analysis of an inclined stay cable under random and periodic support motion excitations

• Ying, Z.G.;Ni, Y.Q.;Duan, Y.F.
• Smart Structures and Systems
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• v.23 no.6
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• pp.641-651
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• 2019
• The stochastic stability control of the parameter-excited vibration of an inclined stay cable with multiple modes coupling under random and periodic combined support disturbances is studied by using the direct eigenvalue analysis approach based on the response moment stability, Floquet theorem, Fourier series and matrix eigenvalue analysis. The differential equation with time-varying parameters for the transverse vibration of the inclined cable with control under random and deterministic support disturbances is derived and converted into the randomly and deterministically parameter-excited multi-degree-of-freedom vibration equations. As the stochastic stability of the parameter-excited vibration is mainly determined by the characteristics of perturbation moment, the differential equation with only deterministic parameters for the perturbation second moment is derived based on the $It{\hat{o}}$ stochastic differential rule. The stochastically and deterministically parameter-excited vibration stability is then determined by the deterministic parameter-varying response moment stability. Based on the Floquet theorem, expanding the periodic parameters of the perturbation moment equation and the periodic component of the characteristic perturbation moment expression into the Fourier series yields the eigenvalue equation which determines the perturbation moment behavior. Thus the stochastic stability of the parameter-excited cable vibration under the random and periodic combined support disturbances is determined directly by the matrix eigenvalues. The direct eigenvalue analysis approach is applicable to the stochastic stability of the control cable with multiple modes coupling under various periodic and/or random support disturbances. Numerical results illustrate that the multiple cable modes need to be considered for the stochastic stability of the parameter-excited cable vibration under the random and periodic support disturbances, and the increase of the control damping rather than control stiffness can greatly enhance the stochastic stability of the parameter-excited cable vibration including the frequency width increase of the periodic disturbance and the critical value increase of the random disturbance amplitude.

### A Study on the Axial Stiffness Prediction of Stand Using Analysis of Variance (분산분석을 이용한 스트랜드의 축강성 예측에 관한 연구)

• Park, Yong-Dae;Yang, Won-Ho;Heo, Seong-Pil;Seong, Gi-Deuk
• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.1
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• pp.127-134
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• 2001
• Wire ropes are widely used in cable car, suspension bridge and elevator, etc. and composed of single or multi-layer strands. It is difficult to find out the characteristics of a strand or wire rope because of complicated geometry and contact condition. In this study, the axial stiffness is evaluated using finite element method and reliable finite element analysis model is presented, taking into consideration the convergence on the length. The axial stiffness predictive equation of a strand is developed using analysis of variance, which can be applicable for characterizing the relationship between load and displacement when the strand configuration is determined.

### Distribution of Natural Frequency of 2-DOF Approximate Model of Stay Cable to Reduction of Area (단면감소에 따른 사장케이블의 2-자유도 근사모델의 고유진동수 분포)

• Joe, Yang-Hee;Lee, Hyun-Chol
• Journal of the Korea institute for structural maintenance and inspection
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• v.18 no.6
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• pp.147-154
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• 2014
• The cable damages of the bridge structures induce very important impact on the structural safety, which implies the close monitoring of the cable damage is required to secure sustained safety of the bridges. Most usual available maintenance techniques are based on the monitoring the change of the natural frequency of the structures by damages. However, existing method are based on vibration method to calculate lateral vibration and system identification can calculate the axial stiffness using sensitivity equation by trial error method. But the frequency study by the longitudinal movement need because of the sag effect in system identification. This study proposes a new method to investigate the damage magnitudes and status. The method improves the accuracies in the magnitudes and status of damages by adopting the natural frequency of longitudinal movement. The study results have been validated by comparing them with the approximate solution of FEM. Thus, the relationship of cable damage and frequency appear with relation that the severe damage has the little frequency. If we know the real frequency we can estimate the cable damage severity using this relationship. This method can be possible the efficient management of the cable damage.

### Stiffness of hybrid systems with and without pre-stressing

• Coupled systems mechanics
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• v.9 no.2
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• pp.147-161
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• 2020
• Constructive merging of "basic" systems of different behavior creates hybrid systems. In doing so, the structural elements are grouped according to the behavior in carrying the load into a geometric order that provides sufficient load and structure functionality and optimization of the material consumption. Applicable in all materializations and logical geometric forms is a transparent system suitable for the optimization of load-bearing structures. Research by individual authors gave insight into suitable system constellations from the aspect of load capacity and the approximatemethod of estimating the participation of partialstiffnesswithin the rigidity ofthe hybrid system. The obtained terms will continue to be the basisfor our own research of the influence of variable parameters on the behavior of hybrid systemsformed of glued laminated girder and cable of different geometric shapes. Previous research has shown that by applying the strut-type hybrid systems can increase the load capacity and reduce the deformability ofthe free girder.The implemented parametric analysis pointsto the basic parameterin the behavior of these systems-the rigidity ofindividual elements and the overallstiffnessofthe system.The basic idea ofpre-stressing is that, in the load system or individual load-bearing element, prior to application of the exploitation load, artificially challenge the forcesthatshould optimize the finalsystembehaviorin the overall load. Pre-stressing is possible only if the supporting system orsystem's element possesssufficientstrength orstiffness, orreaction to the imposed forces of pre-stressing. In this paper will be presented own research of the relationship of partial stiffness of strut-type hybrid systemsofdifferentgeometric forms.Conducted parametric analysisofhybridsystemswithandwithoutpre-stressing, and on the example of the glulam-steel strut-type hybrid system under realistic conditions of change in the moisture content ofthe wooden girder,resulted in accurate expressions and diagramssuitable for application in practice.

### Static and free vibration analysis of shallow sagging inclined cables

• Li, Zhi-Jiang;Li, Peng;He, Zeng;Cao, Ping
• Structural Engineering and Mechanics
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• v.45 no.2
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• pp.145-157
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• 2013
• Based on link-model, we conducted a static analysis and computation of a three-span suspended cable structure in the present paper, and obtained the static configuration and tension distribution of the cable. Using the link and beam model based on finite element method, we analyzed the vibration modal of three-span suspended cable structure, and compared with the results obtained from ANSYS using link and beam element. The vibration modals of shallow sagging inclined cables calculated from proposed method agrees well with ANSYS results, which validates the proposed method. As a result, the influence of bend stiffness on in-plane natural frequencies is much greater than that on out-of-plane natural frequencies of inclined cables.

### A Study on the Bending and Torsional Behaviors of Cable-Stayed Bridges under a Concentrated Moving Load (집중 이동하중을 받는 사장교의 휨 및 비틈 거동에 관한 연구)

• Chang, Sung Pil;Yhim, Sung Soon;Chu, Seok Beom
• Journal of The Korean Society of Civil Engineers
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• v.9 no.3
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• pp.1-12
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• 1989
• The nonlinearity of a cable-stayed bridge results from the large displacement of main girder due to a long span, the catenary action of cables and the flexural stiffness reduced by large axial forces. The dynamic behaviour of a cable-stayed bridge plays an important role in determining its safety. Especially, when the eccentrically moving load is applied to a cable-stayed bridge, the torsional vibration and vertical vibration are coupled and moreover the variation of cable tensions shows important dynamic characteristics. This dissertation presents a theoretical study and a finite element procedure for analysis of a cable-stayed bridge under a eccentrically moving load. Attention is focused on the dynamic behaviours such as dynamic increments of cable tensions and nodal displacements, with the variety of velocities and eccentricities of moving load. It is found that a moving load with eccentricity can have significant effects upon the responses; the torsion of bridge deck and the increments of cable tensions, according to the present results in this study.

### Equivalent Suspension Bridge Model for Tower Design of Multi-span Suspension Bridges (다경간 현수교 주탑 설계를 위한 등가 현수교 모델)

• Choi, Dong-Ho;Na, Ho-Sung;Yi, Ji-Yop;Gwon, Sun-Gil
• Journal of Korean Society of Steel Construction
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• v.23 no.6
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• pp.669-677
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• 2011
• The multi-span suspension bridge generally has more than three towers and two main spans. To economically and effectively design a multi-span suspension bridge, the proper stiffness ratio of the center tower to the side tower must be determined. This study was conducted to propose a method of figuring out briefly the structural behavior of the towers in a multi-span suspension bridge. In the equivalent suspension bridge model, the main cable of the multi-span suspension bridge is idealized as an equivalent cable spring, and the external loads of horizontal and vertical forces that were calculated using the tensile forces of the main cable were applied on top of the towers. The equilibrium equations of the equivalent multi-span suspension bridge model were derived and the equations were solved via nonlinear analysis. To verify the proposed method, a sample four-span suspension bridge with a main span length of 3,000 m was analyzed using thefinite element method. The displacements and moment reactions of each tower in the proposed method were compared with the FEM analysis results. Consequently, the results of the analysis of the equivalent suspension bridge model tended to be consistent with the results of the FEM analysis.

### A STUDY ON NUMERICAL SIMULATION OF TOWED LOW-TENSION CABLE WITH NONUNIFORM CHARACTERISTICS (불균일 단면을 갖는 저장력 예인케이블에 관한 수치해석적 연구)

• Jung, Dong-Ho;Park, Han-Il
• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• pp.161-166
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• 2002
• Low-tension cables have been increasingly used in recent years due to deep-sea developments and the advent of synthetic cables. In the case of low-tension cables, large displacements may happen due to relatively small restoring forces of tension and thus the effects of fluid and geometric non-linearities become predominant. In this study, three-dimensional (3-D) dynamic behavior of a towed low-tension cable with non-uniform characteristics is numerically analyzed by considering fluid and geometric non-linearities and bending stiffness. A Fortran program is developed by employing a finite difference method. In the algorithm, an implicit time integration and Newton-Raphson iteration are adopted. For the calculation of huge size of matrices, block tri-diagonal matrix method is applied, which is much faster than the well-known Gauss-Jordan method in two point boundary value problems. Some case studies are carried out and the results of numerical simulations are compared with a in-house program of WHOI Cable with good agreements.

### Probabilistic Structural Safety Assessment Considering the Initial Shape and Non-linearity of Steel Cable-Stayed Bridges (강사장교의 초기형상과 비선형성을 고려한 확률론적 구조안전성 평가)

• Bang, Myung-Seok;Han, Sung-Ho;Lee, Woo-Sang;Lee, Chin-Ok
• Journal of the Korean Society of Safety
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• v.25 no.3
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• pp.91-99
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• 2010
• In this study, the advanced numerical algorithm is developed which can performed the static and dynamic stochastic finite element analysis by considering the effect of uncertainties included in the member stiffness of steel cable-stayed bridges and seismic load. After conducting the linear and nonlinear initial shape analysis, the advanced numerical algorithm is the assessment tool which can performed structural the response analysis considering the static linearity and non-linearity of before or after induced intial tensile force, and examined the reliability assessment more efficiently. The verification of the developed numerical algorithm is evaluated by analyzing the regression analysis and coefficient of correlation using the direct monte carlo simulation. Also, the dynamic response characteristic and coefficient of variation of the steel cable-stayed bridge is calculated by considering the uncertainty of random variables using the developed numerical algorithm. In addition, the quantitative structural safety of the steel cable-stayed bridges is evaluated by conducting the reliability assessment based upon the dynamic stochastic finite element analysis result.

### Damping and frequency of twin-cables with a cross-link and a viscous damper

• Zhou, H.J.;Yang, X.;Peng, Y.R.;Zhou, R.;Sun, L.M.;Xing, F.
• Smart Structures and Systems
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• v.23 no.6
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• pp.669-682
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• 2019
• Vibration mitigation of cables or hangers is one of the crucial problems for cable supported bridges. Previous research focused on the behaviors of cable with dampers or crossties, which could help engineering community apply these mitigation devices more efficiently. However, less studies are available for hybrid applied cross-ties and dampers, especially lack of both analytical and experimental verifications. This paper studied damping and frequency of two parallel identical cables with a connection cross-tie and an attached damper. The characteristic equation of system was derived based on transfer matrix method. The complex characteristic equation was numerically solved to find the solutions. Effects of non-dimensional spring stiffness and location on the maximum cable damping, the corresponding optimum damper constant and the corresponding frequency of lower vibration mode were further addressed. System with twin small-scale cables with a cross-link and a viscous damper were tested. The damping and frequency from the test were very close to the analytical ones. The two branches of solutions: in-phase modes and the out-of-phase modes, were identified; and the two branches of solutions were different for damping and frequency behaviors.