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In order to study the coupling vibration between a bridge and a train under the action of crosswind loads, a dynamic interaction model of the wind–train–bridge system is established considering the geometric nonlinear factors of a long-span suspension bridge. A calculation frame is composed, and a corresponding computer program is written. A long-s...
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This paper systematically studies the nonlinear dynamic response and stability properties of the submerged tensioned anchor cable (STAC) considering the coupling effect of the parametric vibration and vortex-induced vibration. A refined and universal modeling approach for the STAC is suggested to describe the structural mechanical behavior more exa...
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... It is the key load-bearing component of the bridge, and its failure will cause the instability of bridge structure or even collapse [1,2]. In the service process, the suspension bridge is subjected to the coupling action of the dead load (stiffened beam, deck system, main cable, etc.), the wind load, the live load (automobile load, etc.) and the salt spray environment (NaCl, MgCl 2 , etc.) [3][4][5][6]. These lead to the friction, corrosion, and fatigue behaviors between the parallel wires inside the main cable at the main saddle. ...
The main cable bent around the saddle of the suspension bridge is subjected to the wind, the vehicle, the bridge’s own weight and the corrosive media. The coupling of the three loads and the environments causes the friction, the corrosion, and the fatigue (tribo-corrosion-fatigue) among the wires inside the main cable. In this paper, a wire bending tribo-corrosion-fatigue test rig was designed and developed. The effect of fatigue load on the bending friction behaviors between the cable wires in ultrapure water and 3.5% NaCl solution was explored. The tribological properties and electrochemical corrosion behaviors under different fatigue loading ranges were investigated. The tribo-corrosion-fatigue interaction between the cable wires was quantitatively characterized, and the mechanism of the interaction was analyzed. The results demonstrate that the increasing fatigue load exacerbates the coupling damage of the cable wires attributed to the enhanced interaction. The findings carry theoretical importance when assessing the main cable’s deterioration and the load-bearing safety of a suspension bridge.
... However, it is very complicated for the finite-terms Galerkin discrete model or the direct perturbation method to obtain the solutions for the nonlinear equations. In fact, the most convenient and effective method of solving the mechanical problems of continuous structures is the finite element method [30][31][32][33][34][35][36]. This method is widely used in static and dynamic problems of structures [33][34][35][36]. ...
A common strategy for studying the nonlinear vibrations of beams is to discretize the nonlinear partial differential equation into a nonlinear ordinary differential equation or equations through the Galerkin method. Then, the oscillations of beams are explored by solving the ordinary differential equation or equations. However, recent studies have shown that this strategy may lead to erroneous results in some cases. The present paper carried out the following three research studies: (1) We performed Galerkin first-order and second-order truncations to discrete the nonlinear partial differential integral equation that describes the vibrations of a Bernoulli-Euler beam with initial curvatures. (2) The approximate analytical solutions of the discretized ordinary differential equations were obtained through the multiple scales method for the primary resonance. (3) We compared the analytical solutions with those of the finite element method. Based on the results obtained by the two methods, we found that the Galerkin method can accurately estimate the dynamic behaviors of beams without initial curvatures. On the contrary, the Galerkin method underestimates the softening effect of the quadratic nonlinear term that is induced by the initial curvature. This may cause erroneous results when the Galerkin method is used to study the dynamic behaviors of beams with the initial curvatures.
... Lateral pretension cables can improve the aerodynamic stability of small-stiffness suspension bridges [18]. The vibrations of suspension bridges on complex loads, such as wind and heavy vehicle loads, still need further research [19]. Recent studies suggested that the vortex-excited vibrations of cylinders are not fully understood. ...
... Equation (19) shows that the static wind load produces a static deformation, f 0 U 2 /ω 2 . This deformation is inversely proportional to the linear stiffness of the bridge. ...
... This also means that the present research ignores the effect of the static wind load on the natural frequency of the bridges. Substituting Equation (19) into Equation (17) obtains ...
A low stiffness makes long-span suspension bridges sensitive to loads, and this sensitivity is particularly significant for wind-induced nonlinear vibrations. In the present paper, nonlinear vibrations of suspension bridges under the combined effects of static and vortex-induced loads are explored using the nonlinear partial differential–integral equation that models the plane bending motion of suspension bridges. First, we discretized the differential–integral equation through the Galerkin method to obtain the nonlinear ordinary differential equation that describes the vortex-induced vibrations of the bridges at the first-order symmetric bending mode. Then, the approximate analytical solution of the ordinary differential equation was obtained using the multiple scales method. Finally, the analytical solution was applied to reveal the relationships between the vibration amplitude and other parameters, such as the static wind load, the frequency of dynamic load, structural stiffness, and damping. The results show that the static wind load slightly impacts the bridge’s vibrations if its influence on the natural frequency of bridges is ignored. However, the bridge’s vibrations are sensitive to the load frequency, structural stiffness, and damping. The vibration amplitude, as a result, may dramatically increase if the three parameters decrease.
In order to prevent skid accidents of main cable of suspension bridge, dynamic contact behaviors between saddle materials and steel wires were explored in the present study. Dynamic contact tests of saddle materials were conducted employing the self-made dynamic contact test rig. Dynamic contact behaviors of the saddle material (transverse slip, longitudinal deformation, contact state, wear mechanism) in a friction cycle were investigated. Effects of transverse and longitudinal locations, friction cycles and saddle materials on the dynamic contact behaviors were presented. The results show that dynamic contact states between saddle specimen and steel wireexhibits the adhesion-gross slip-adhesion-gross slip state in a friction cycle. The transverse slip and longitudinal deformation of saddle specimen both decrease with increasing distance to the contact interface, decrease along the transverse sliding direction, and increase with increasing friction cycles. The ZG270-480 saddle material exhibits the largest average transverse slip and longitudinal deformation, while ZG275-485 saddle material shows the smaller values.
The long-span multi-tower suspension bridge is widely used in the construction of river and sea crossing bridges. The load-bearing safety and anti-sliding safety of its main cable are directly related to the structural safety of a suspension bridge. Failure mechanisms of the main cable of a long-span multi-tower suspension bridge are discussed. Meanwhile, the tribo-corrosion-fatigue of main cable, contact, and slip behaviors of the saddle and service safety assessment of the main cable are reviewed. Finally, research trends in service safety assessment of main cable are proposed. It is of great significance to improve the service safety of the main cable and thereby to ensure the structural safety of long-span multi-tower suspension bridges.
