# Analysis of Vehicle-Bridge Coupling Vibration Characteristics of Curved Girder Bridges
## 1 Introduction  
Compared to straight girder bridges, curved bridges exhibit significant \"bending torsion coupling\" due to the influence of curvature radius. Under load, the main girder generates a bending moment and torque, and the stress performance significantly differs to straight bridges [1, 2, 3]. At the same time, due to the vehicle's movement along the curve, the reference coordinate system for establishing the car vibration equation is constantly changing. The setting of the bridge deck superelevation and the existence of centrifugal force make the radial vibration of the vehicle-bridge coupling system along the curve aspects that cannot be ignored. The coupling relationship of curved girder bridges is more complex than that of straight bridges [4, 5]. There are many studies on the coupling vibration of vehicles and bridges in straight bridges [6, 7]. The coupling effect is different as the vehicle moves. [PERSON] focused on vehicles moving on the bridge, investigated the changes in frequencies and modes of vibration of a vehicle-bridge system, and found that the varying vehicle positions had obvious influences on the modal properties of the vehicle and bridge [8]. [PERSON] carried out a test and studied different load conditions of vehicles stationed over the bridge deck, and proposed that it is necessary to address the vehicle-bridge interaction model to capture the accurate bridge dynamic response [9]. [PERSON] presented results suggesting that the eccentric vertical and lateral forces are the major excitation sources in vehicle-bridge coupling analysis [10], and relatively detailed research results were achieved. The method can be applied to analyzing curved beam bridges by\"using straight instead of curved.\" For example, [PERSON] et al. [11] studied the coupling vibration characteristics and mechanisms of trains and small radius curved section groove beam bridges using the bisector method with a straight instead of curved arrangement, and with a curved railway simple-supported groove girder bridge located at a radius of 300m as the object. [PERSON] et al. [12] used linear beam elements to approximate curved girder bridges and analyzed the impact of factors such as the number of lanes, deck smoothness, vehicle speed, and vehicle type on the impact coefficient. [PERSON] et al. [13] adopted the processing method of replacing \"curves\" with \"straight lines\" to establish a two-axis seven-degree-of-freedom vehicle model. [PERSON] studied the level of road roughness and the relationship between road smoothness and wheel slip and jump, and found that higher levels of road roughness make it easier for jump and other phenomena to occur [14]. The \"using straightness to replace curvature\" analysis method has high computational efficiency. However, due to the lack of full consideration of the influence of curvature, it cannot accurately analyze the longitudinal and lateral vibration coupling mechanical behavior and bending-torsional coupling effect of curved girder bridges under the action of vehicles. However, compared to straight bridges, some curved girder bridges (such as road interchange ramps) have characteristics such as the inward inclination of the bridge surface, widening of the outer side, resulting in no vertical symmetry axis of the girder section, noticeable bending-torsional coupling effect, and centrifugal effect of the vehicles. The vehicle-bridge coupling vibration mechanism is complex, and more fundamental studies in this area and limited applications are needed [15]. This article utilized the vehicle-bridge coupling vibration analysis method for straight bridges, theoretically analyzed the vehicle-bridge coupling relationship for curved girder bridges, and used curved girder units to simulate curved girder bridges.