## 1 Introduction  
The natural frequencies, damping, and free vibration features of principal modes of bridge structures are the basis for analyzing the dynamic characteristics of cable-stayed bridges. The dynamic characteristics of bridge structures depend heavily on the stiffness, supporting conditions, and composition system of the structures. Studies on the dynamic characteristics of bridge structures are important for wind stability analysis, seismic design, health inspection, and maintenance of bridge structures [1,2]. At the same time, it is also an important basis to judge whether a bridge structure is intact or not. With the development of modern bridge technology, bridge development tendencies have become more and more beautiful, complex, and bigger. A single cable-plane cable-stayed bridge is popular because of its advantages, such as beautiful aesthetics, good perspective, navigation, and flood discharge performance. However, a single cable plane structure does not provide enough resistance to torsion capability, which reduces the torsional rigidity of the structure and wind resisting stability. Its dynamic characteristics need to be studied carefully. If the tower style of a bridge is a single tower, it can reduce costs and increase the sense of beauty. At the same time, it can increase structural flexibility, the risk of wind resistance, and anti-seismic performance. For a single-tower cable-stayed bridge, the auxiliary piers in the side span are helpful to improve the overall rigidity of the structure. For a long-span steel truss girder cable-stayed bridge, the side girder of the steel truss is the largest component which bears the axial force and bending moment, and the force always is the most unfavorable [3,4]. The tension diagonal and crossbeam are the main force members of a steel truss beam. The web members play a stabilizing role. For a cable-stayed bridge with a single central cable plane, the maximum cantilever state is the most unfavorable construction stage and is critical to the closure control. Therefore, the dynamic characteristics of a steel truss girder cable-stayed bridge with single tower and single cable plane should be analyzed. Through finite element modeling, the dynamic characteristics of bridges can be optimized by modifying different bridge parameters [5, 6, 7, 8, 9]. For example, the stiffness [10,11] of each member of a bridge, the constraint conditions [12] of different members and pylons, the influence of concentrated force [13], and the position of auxiliary piers [14] will have a certain impact on the dynamic characteristics of the bridge. At present, in-depth studies on the dynamic characteristics of bridges have been conducted; however, most studies have been aimed at mainstream bridge types. A cable-stayed bridge with single tower and single cable plane is a unique type of bridge, and there is still a lack of relevant studies. Therefore, the main focus of this study is to investigate the effect of changes in component stiffness, cable inclination angle, and auxiliary piers position on the dynamic characteristics of a single tower and single cable plane cable-stayed bridge and how to optimize them. [PERSON] et al. [15] systematically studied the dynamic characteristics of a self-anchored suspension bridge, which is a concrete bridge with a wide deck, and its transverse vibration is worth studying. [PERSON]. [PERSON] et al. [16] conducted an in-depth study on the dynamic characteristics of the Colquitz river bridge, and the main research direction was to evaluate the seismic resistance of the bridge structure. [PERSON] and [PERSON] [17] focused on the dynamic characteristics of continuous beam bridges. Although multi-span continuous beam technology is very mature, there are few long-span multi-span continuous beams, which have generally been replaced by cable-stayed bridges or suspension bridges, and still have research value. [PERSON] et al.