• Korean Journal of Mathematics
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• v.16 no.3
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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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• v.30 no.5
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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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• v.76 no.3
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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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• v.72 no.2
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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.

• Journal of the Korea institute for structural maintenance and inspection
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• v.2 no.2
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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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.5A
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• pp.699-707
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• 2008

For most structural evaluation of bridge integrity, it is very important to measure the geometric profile, which is a major factor representing the global behavior of civil structures, especially bridges. In the past, because of the lack of appropriate methods to measure the deflection profile of bridges on site, the measurement of deflection has been restricted to just a few discrete points along the bridge, and the measuring points have been limited to the locations installed with displacement transducers. Thus, some methods for predicting the static deflection by using fiber optic strain sensors has been applied to simply supported bridges. In this study, a method of estimating the static deflection profile by using strains measured from suspension bridges was proposed. Based on the classical deflection theory of suspension bridges, an equation of deflection profile was derived and applied to obtain the actual deflection profile on Namhae suspension bridge. Field load tests were carried out to measure strains from FBG strain sensors attached inside the stiffening girder of the bridge. The predicted deflection profiles were compared with both precise surveying data and numerical analysis results. Thus, it is found that the equation of predicting the deflection profiles proposed in this study could be applicable to suspension bridges and the FBG strain sensors could be reliable on acquiring the strain data from bridges on site.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.115-122
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• 1995

• Korean Journal of Mathematics
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• v.3 no.1
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• pp.59-70
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• 1995

• Proceedings of the Materials Research Society of Korea Conference
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• 2010.05a
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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.

• Proceedings of the KSR Conference
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• 2005.11a
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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.