• Journal for History of Mathematics
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• v.20 no.4
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• pp.93-104
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• 2007

It is well known that a suspension bridge may display certain oscillations under external aerodynamic forces. Under the action of a strong wind, in particular, a narrow and very flexible suspension bridge can undergo dangerous oscillations. The collapse of the Tacoma Narrows suspension bridge caused by a wind blowing at a speed of 42 miles per hour, is one of the most striking examples. In this paper, we study models describing oscillations in suspension bridges and known results.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.107-116
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• 2005

A suspension bridge is an example of a nonlinear dynamical system, especially systems with the so called jumping nonlinearity. The fact that we deal with a serious and topical problem is demonstrated for example by the collapse of the Tacoma Narrow suspension bridge. So it would be very contributive to determine under what conditions a similar situation cannot occur and find out safe parameters of the bridge construction. In this paper, we show various possibilities how to model the behaviour of suspension bridge. Then we introduce our own results concerning existence and uniqueness of time-periodic solutions.

• Journal of the Earthquake Engineering Society of Korea
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• v.8 no.6 s.40
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• pp.1-11
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• 2004

In the previous study(1), the finite element method was used for the vertical vibration analysis of suspension bridge considering the effects of the shear deformation and the rotary inertia under moving load. This study firstly performs the eigenvalue analysis for the free vertical vibration of suspension bridge using FEM analysis. Next the equations of motion considering interaction between suspension bridge and vehicles/train are derived using mode superposition method. And dynamic analysis was performed using the Newmark $\beta$ Method. Finally through the numerical examples, the dynamic responses of bridges by this study are investigated.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.1
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• pp.49-60
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• 2014

For simple and accurate analysis for behaviors of multi-span suspension bridges which are expected to be frequently constructed as strait-crossing bridges, the deflection theory as the peculiar theory of a suspension bridge can be applied. This paper performs a structural analysis for four-span suspension bridges using the deflection theory. Simply-supported beams with tension are used for girders and the deflections of the beams due to the vertical loads and moments at supports are calculated. The calculation is performed iteratively until the deflections satisfy the compatibility equations of cables. The results of the deflection theory analysis considering tower rigidity are compared with those of the finite element analysis for verification. Importance of the tower rigidity for four-span suspension bridges is confirmed using various compatibility equations of the cable due to variation of the constraint conditions between main cable and top of towers. In addition, the simple parametric analysis for variation of the center tower rigidity is performed.

• 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.

• Journal of Industrial Technology
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• v.17
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• pp.125-130
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• 1997

이 논문에서는 비선형 빔방정식을 이용할 수 있는 현수교방정식의 존재하는 해의 개수를 조사하였다. 외부에서 주어지는 함수가 주기함수일 경우에 나타나는 여러 가지 성질들을 조사하였으며 주어진 항들의 계수가 상수인 경우 어떤 범위에서 몇 개의 해가 존재할 수 있는지를 조사하였다. Leray-Schauder degree를 이용하여 존재할 수 있는 해의 개수를 판별하는 근거로 삼았다. 특히 일정한 항의 계수가 변수를 포함하는 경우에 나타날 수 있는 변화에 대하여 조사하였다.

• Journal of the Korea Computer Industry Society
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• v.7 no.1
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• pp.33-38
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• 2006

The motions of suspension bridge as well as hanging cable are governed by nonlinear partial differential equations. Nonlinearity gives rise to a large amplitude oscillation. We use finite difference methods to compute periodic solutions to the torsional partial differential equations. We use the one-noded forcing term and a slight perturbation in the forcing term.

• Journal of the Korea Computer Industry Society
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• v.3 no.5
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• pp.569-574
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• 2002

We model the torsional oscillation of a suspension bridge, which is the forced sine-Cordon equation on a bounded domain. We use finite difference method to solve nonlinear partial differential equation numerically. The partial differential equation has multiple periodic solutions. Whether the span oscillates with small or large amplitude depends oかy on its initial displacement and velocity. Moreover, we observe that the qualitative properties are consistent with the behavior observed at the Tacoma Narrows Bridge on the day of its collapse.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.8 no.2
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• pp.185-196
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• 1988

In this study, a method of nonlinear dynamic analysis of suspension bridges subjected to random wind loads is pre.sented. The nonlinearity considered is the one due to the interaction between the motion of the bridge girder and the tertsion variation of the main cables. The equation of motion is formulated using a continuum approach. The coupling between the vertical and torsional motions are included in the analysis. The equation of motion is solved by using the mode superposition method. The analysis is carried out in the frequency domain utilizing the stochastic linearization technique on to the modal equations. In the linearization procedure, the nonlinear terms are approximated as linear ones with constant terms. The verification of the method has been performed on a case with four modal degrees of freedom. Example analyses are carried out on two suspension bridges for various wind speeds and wind force parameters. Numerical results indicate that, by including the nonlinearity into the analysis, the dynamic responses of the bridges, particularly in the vertical direction, change considerably.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.4 s.70
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• pp.361-372
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• 2005

In the previous study(Kim 등, 2004), the finite element method was used for the vortical vibration analysis of suspension bridge with the effects of the shear deformation and the rotary inertia under moving load considering the bridge-vehicle interaction. The purpose of this study is to investigate the effect of an eccentric vehicle and shear deformation. So we firstly performs the eigenvalue analysis for the free vortical and the torsional vibration of suspension bridges using FEM analysis. Next the equations of motion considering interaction between suspension bridges and vehicles/trains are derived using the mode superposition method. And then dynamic analysis was performed using the Newmark method. Finally through the numerical examples, the dynamic responses of bridges are investigated according to the proposed procedure.