• Korean Journal of Mathematics
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• v.15 no.1
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• pp.1-11
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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. 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 investigate relations between the multiplicity of solutions and nonlinear terms in this suspension bridge equation using critical point theorem and linking theorem.

• 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 of the Korea Computer Industry Society
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• v.5 no.3
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• pp.355-362
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• 2004

This paper presents the common and different results between the galloping cable and torsional oscillations in suspension bridge. Numerical results of the galloping cable and torsional oscillations in suspension bridge are presented by using the second-order Runge Kutta method under the initial conditions. This paper shows that large amplitude solution can coexist with the small amplitude one as the frequency and amplitude of the oscillation change. The differences in symmetry and transient effects are presented.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.6
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• pp.463-470
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• 2013

In this paper, 2D simple analyses were performed in order to predict the large torsional oscillations in a suspension bridge based on Makenna and Tuama model(2001). The existing model(Makenna and Tuama, 2001) has shown unrealistic results as the wind speed increases and frequency decreases. Furthermore, resonance could not be simulated by the existing model. Therefore, in this study, new model was proposed with a consideration of the torsional resistance. The vertical and rotational behaviors of the deck in the suspension bridge were analyzed. Analysis results showed that at first vertical oscillations were observed and it was gradually transformed to the rotation oscillations. With the consideration of the torsional resistance, it was shown that vertical behavior were stabilized as time passed. However, the rotational behavior was not stabilized and was kept until the end of analysis. Beat periods decreased while the wind speed increased. The resonance of the rotational mode was dependent to the rotational resistance. Obtained results could be applied for the design of the suspension bridge under the wind load.

• Wind and Structures
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• v.6 no.6
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• pp.451-470
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• 2003

The classical two-degree-of-freedom (2-d-o-f) "sectional model" is of common use to study the dynamics of suspension bridges. It takes into account the first pair of vertical and torsional modes of the bridge and describes well global oscillations caused by wind actions on the deck, yielding very useful information on the overall behaviour and the aerodynamic and aeroelastic response; however, it does not consider relative oscillations between main cables and deck. On the contrary, the 4-d-o-f model described in the two Parts of this paper includes longitudinal deformability of the hangers (assumed linear elastic in tension and unable to react in compression) and thus allows to take into account not only global oscillations, but also relative oscillations between main cables and deck. In particular, when the hangers go slack, large nonlinear oscillations are possible; if the hangers remain taut, the oscillations remain small and essentially linear: the latter behaviour has been the specific object of Part I (Sepe and Augusti 2001), while the present Part II investigates the nonlinear behaviour (coexisting large and/or small amplitude oscillations) under harmonic actions on the cables and/or on the deck, such as might be generated by vortex shedding. Because of the discontinuities and strong nonlinearity of the governing equations, the response has been investigated numerically. The results obtained for sample values of mechanical and forcing parameters seems to confirm that relative oscillations cannot a priori be excluded for very long span bridges under wind-induced loads, and they can stimulate a discussion on the actual possibility of such phenomena.

• Wind and Structures
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• v.4 no.1
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• pp.1-18
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• 2001

The classical two-degree-of-freedom (2-d-o-f) "sectional model" is currently used to study the dynamics of suspension bridges. Taking into account the first pair of vertical and torsional modes of the bridge, it describes well global oscillations caused by wind actions on the deck and yields very useful information on the overall behaviour and the aerodynamic and aeroelastic response, but does not consider relative oscillation between main cables and deck. The possibility of taking into account these relative oscillations, that can become significant for very long span bridges, is the main purpose of the 4-d-o-f model, proposed by the Authors in previous papers and fully developed here. Longitudinal deformability of the hangers (assumed linear elastic in tension and unable to react in compression) and external loading on the cables are taken into account: thus not only global oscillations, but also relative oscillations between cables and deck can be described. When the hangers go slack, large nonlinear oscillations are possible; if the hangers remain taut, the oscillations are small and essentially linear. This paper describes the model proposed for small and large oscillations, and investigates in detail the limit condition for linear response under harmonic actions on the cables (e.g., like those that could be generated by vortex shedding). These results are sufficient to state that, with geometric and mechanical parameters in a range corresponding to realistic cases of large span suspension bridges, large relative oscillations between main cables and deck cannot be excluded, and therefore should not be neglected in the design. Forthcoming papers will investigate more general cases of loading and dynamic response of the model.

• Structural Engineering and Mechanics
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• v.55 no.2
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• pp.365-377
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• 2015

Large-amplitude vibration of overhead sign structures can cause unfavorable psychological responses in motorists, interfere with readability of the signs, and lead to fatigue cracking in the sign structures. Field experience in Texas suggests that an overhead sign structure can vibrate excessively when supported within the span of a highway bridge instead of at a bent. This study used finite element modeling to analyze the dynamic displacement response of three hypothetical sign structures subjected to truck-passage-induced vertical oscillations recorded for the girders from four actual bridges. The modeled sign bridge structures included several span lengths based on standard design practices in Texas and were mounted on precast concrete I-girder bridges. Results revealed that resonance with bridge girder vertical vibrations can amplify the dynamic displacement of sign structures, and a specific range of frequency ratios subject to undesirable amplification was identified. Based on these findings, it is suggested that this type of sign structure be located at a bridge bent if its vertical motion frequency is within the identified range of bridge structure excitation frequencies. Several alternatives are investigated for cases where this is not possible, including increasing sign structure stiffness, reducing sign mass, and installing mechanical dampers.

• Structural Engineering and Mechanics
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• v.46 no.5
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• pp.713-734
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• 2013

Bridges are vital components of the railroads. High speed of travel, the periodic and oscillatory nature of the loads and the comparable vehicle bridge weight ratio distinguish the railway bridges from the road bridges. The close proximity between estimations by some numerical methods and the measured data for the bridge-vehicle dynamic response under the moving load conditions has boosted the confidence in the numerical analyses. However, there is hardly any report regarding the responses of the railway bridges under the effect of the trains entering from the opposite directions while running at unequal speed and having dissimilar geometries. It is the purpose of this article to present an analytical method for the dynamic analysis of the railway bridges under the influence of two opposing series of moving loads. The bridge structural damping and many modes of vibrations are included. The concept of modal superposition is used to solve for the system motion equations. The method of solution is indeed a computer assisted analytical solution. It solves for the system motion equations and gives output in terms of the bridge deflection. Some case studies are also considered for the validation of the proposed method. Furthermore, the effects of varying some parameters such as the distance between the bogies, and the bogie wheelset distance are studied. Also, the conditions of resonance and cancellation in the dynamic response for a variety of vehicle-bridge specifications are investigated.

• International Journal of Control, Automation, and Systems
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• v.5 no.3
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• pp.223-233
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• 2007

Crane payloads frequently swing with large amplitude motion that degrades safety and throughput. Open-loop methods have addressed this problem, but are not effective for disturbances. Closed-loop methods have also been used, but generally require the speed of the driving motors to be precisely controlled. This paper develops a feedback control method for controlling motors to cancel the measured payload oscillations by intelligently timing the ensuing on and off motor commands. The effectiveness of the oscillation suppression scheme is experimentally verified on an industrial bridge crane.

• Wind and Structures
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• v.19 no.3
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• pp.233-247
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• 2014

Vortex-induced oscillation is a type of aeroelastic phenomenon, to which extended structures such as long-span bridges are most susceptible. The vortex-induced vibration (VIV) behaviors of a concerned bridge were investigated conventionally in virtue of wind tunnel tests on string-mounted sectional models. This necessitates the building of a linkage between the response of the sectional model and that of the prototype structure. Although many released literatures have related to this issue and provided suggestions, there is a lack of consistency among them. In this study, some theoretical models describing the vortex-induced structural motion, including the linear empirical model, the nonlinear empirical model and the modified (or generalized) nonlinear empirical model, are firstly reviewed. Then, the concept of equivalent mass density is introduced based on the principle that an equal input of energy should result in identical structural amplitudes. Based on these, the theoretical linkages between the amplitude of a section model and that corresponding to the prototype bridge are discussed with different analytical models. Theoretical derivation indicates that such connections are dependent mainly on two factors, one is the presupposed shape of deformation, and the other is the theoretical VIV model employed. The theoretical analysis in this study shows that, in comparison to the nonlinear empirical models, the linear one can result in obvious larger estimations of the full bridges' responses, especially in cases of cable-stayed bridges.