• Korean Journal of Mathematics
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• 제16권3호
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• pp.355-362
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• 2008

We prove the existence of a unique positive solution for a class of systems of the following nonlinear suspension bridge equation with Dirichlet boundary conditions and periodic conditions $$\{{u_{tt}+u_{xxxx}+\frac{1}{4}u_{ttxx}+av^+={\phi}_{00}+{\epsilon}_1h_1(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\{v_{tt}+v_{xxxx}+\frac{1}{4}u_{ttxx}+bu^+={\phi}_{00}+{\epsilon}_2h_2(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ where $u^+={\max}\{u,0\},\;{\epsilon}_1,\;{\epsilon}_2$ are small number and $h_1(x,t)$, $h_2(x,t)$ are bounded, ${\pi}$-periodic in t and even in x and t and ${\parallel} h_1{\parallel}={\parallel} h_2{\parallel}=1$. We first show that the system has a positive solution, and then prove the uniqueness by the contraction mapping principle on a Banach space

• Structural Engineering and Mechanics
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• 제30권5호
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• pp.559-576
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• 2008

Having established the initial geometry and cable force of a typical three span suspension bridge under permanent load, the additional maximum response of the cable and the stiffening girder due to live load are determined, by means of an analytic procedure, considering the girder first hinged at its ends and then continuous through the main towers. The problem of interaction between the cable and the stiffening girder is examined taking under due consideration the second order effects, whereby, through the analogy to a fictitious tensioned beam under transverse load, a closed -form solution is achieved by means of a simple quadratic equation. It is found that the behavior of the whole system is governed by five simple dimensionless parameters which enable a quick determination of all the relevant design magnitudes of the bridge. Moreover, by introducing these parameters, a set of diagrams is presented, which enable the estimation of the influence of the geometric and loading data on the response and permit its immediate evaluation for preliminary design purposes.

• Structural Engineering and Mechanics
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• 제76권3호
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• pp.293-310
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• 2020

This study derives the differential equations of free vertical bending and torsional vibrations for two- and three-pylon suspension bridges using d'Alembert's principle. The respective algorithms for natural vibration frequency and vibration mode are established through the separation of variables. In the case of the three-pylon suspension bridge, the effect of the along-bridge bending vibration of the middle pylon on the vertical bending vibration of the entire bridge is considered. The impact of torsional vibration of the middle pylon about the vertical axis on the torsional vibration of the entire bridge is also analyzed in detail. The feasibility of the proposed method is verified by two engineering examples. A comparative analysis of the results obtained via the proposed and more intricate finite element methods confirmed the former feasibility. Finally, the middle pylon stiffness effect on the vibration frequency of the three-pylon suspension bridge is discussed. It is found that the vibration frequencies of the first- and third-order vertical bending and torsional modes both increase with the middle pylon stiffness. However, the increase amplitudes of third-order bending and torsional modes are relatively small with the middle pylon stiffness increase. Moreover, the second-order bending and torsional frequencies do not change with the middle pylon stiffness.

• Structural Engineering and Mechanics
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• 제72권2호
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• pp.169-180
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• 2019

The underlying mechanism of the wind-induced vibration of the hangers of the suspension bridges is still not fully understood at present and hence is comprehensively examined in this study. More specifically, a series of field measurements on the No. 2 hanger of the Xihoumen Bridge was first carefully conducted. Large amplitude vibrations of the hanger were found and the oscillation amplitude of the leeward cable was obviously larger than that of the windward cables. Furthermore, the trajectory of the leeward cable was close to an ellipse, which agreed well with the major characteristics of wake-induced vibration. Then, a theoretical model for the wake-induced vibration based on a 3-D continuous cable was established. To obtain the responses of the leeward cable, the finite difference method (FDM) was adopted to numerically solve the established motion equation. Finally, numerical simulations by using the structural parameters of the No. 2 hanger of the Xihoumen Bridge were carried out within the spatial range of $4{\leq}X{\leq}10$ and $0{\leq}Y{\leq}4$ with a uniform interval of ${\Delta}X={\Delta}Y=0.25$. The results obtained from numerical simulations agreed well with the main features obtained from the field observations on the Xihoumen Bridge. This observation indicates that the wake-induced vibration might be one of the reasons for the hanger oscillation of the suspension bridge. In addition, the effects of damping ratio and windward cable movement on the wake-induced vibration of the leeward cable were numerically investigated.

• 한국구조물진단유지관리공학회 논문집
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• 제2권2호
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• pp.177-184
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• 1998

The equation of motion on the vehicle-bridge system is established as the simultaneous equations which are combined the equation of vehicle and bridge by the interaction elements. A vehicle element is modeled as lumped masses supported by springs and dashpots, and a bridge element with pavement roughness is modeled as beam elements. An interaction element is defined to consist of a bridge element and the suspension units of the vehicle resting on the element. By the dynamic condensation method, the degrees of the freedom are eliminated, and compared with all the degrees of freedom on the bridge, the efforts of calculation is decreased. Thus, although a very small computational error is occured, the present technique appears to be computationally more efficient. It is particularly suitable for the simulation of bridges with a series of vehicles moving on the deck.

• 대한토목학회논문집
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• 제28권5A호
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• pp.699-707
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• 2008

교량구조물의 안전성 평가에 있어서 처짐형상을 측정하는 것은 매우 중요한 요소이다. 그러나 교량의 처짐을 측정하는 작업은 일반적으로 용이하지 않으며, 경우에 따라서 측정점이 제한되거나 많은 비용이 소요된다. 따라서 최근에 광섬유 변형률센서를 이용한 교량의 처짐형상을 간접적으로 추정하는 연구가 진행되고 있으나 단순지지 형식의 교량에 주로 적용되고 있다. 본 연구에서는 현수교의 고전적인 처짐이론을 적용하여 측정된 변형률로부터 처짐형상을 추정하는 기법을 제시하였으며, 이에 대한 검증을 위하여 남해대교를 대상으로 현장 재하시험을 수행하였다. 남해대교 보강형 내부에 부착한 FBG 변형률센서를 이용하여 변형률을 계측하였으며, 제안한 추정기법을 적용하여 얻어진 처짐형상을 정밀측량데이터 및 구조해석결과와 비교분석하였다. 결과적으로 본 연구에서 제안한 현수교 처짐형상 추정기법의 적용가능성을 검증하였으며, FBG 변형률센서의 현장 적용성을 확인하였다.

• 대한수학회논문집
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• 제10권1호
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• pp.115-122
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• 1995

• Korean Journal of Mathematics
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• 제3권1호
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• pp.59-70
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• 1995

• 한국재료학회:학술대회논문집
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• 한국재료학회 2010년도 춘계학술발표대회
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• pp.23.2-23.2
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• 2010

Researches on the drying of particle/polymer suspensions receive attentions in technical applications such as manufacturing display and batteries. In this study, the effect of polymers on drying behavior of silica/poly(vinyl alcohol) suspension was investigated in terms of suspension stability and stress development during drying. The effect of polymer adsorption was studied by changing pH. More strongly flocculated suspension with lower pH became more dispersed and close-packed film after drying. Evaluation of potential energy allows us to suggest that the adsorbed polymers which bridge the particles introduce steric repulsion and lead flocculated suspension to dispersed film. When the effect of adsorption kinetics was studied by changing the mixing time, the adsorption amount, characteristic stress and dried film density showed a similar behavior in the form of with a single characteristic time. It implies that the drying process can be determined by simple characteristic equation with a single time constant.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2005년도 추계학술대회 논문집
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• pp.1177-1183
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• 2005

This paper presents the effects of dynamic response of the railway bridge through the suspension system when the train is moving with uniform speed and non-uniform speed Railway bridges are subjected to dynamic loads generated by the interaction between moving vehicles and the bridge structures. these dynamic loads result in response fluctuation in bridge members. To investigate the real dynamic behavior of the bridge, a number of analytical and experimental investigation should be carried out. This paper, a train/bridge interaction analysis program considerate braking action. New scheme consideration of braking action on the bridge using speed-dependent braking function is presented. This program also used torsional degree of freedom and constraint equation based on geometrical relationship in order to take into consideration three-dimensional eccentricity effect due to the operation on double track through quasi three-dimensional analysis.