# Research on an Improved Method for Galloping Stability Analysis Considering Large Angles of Attack
## 1 Introduction
[PERSON] proposed a mathematical model for unsteady galloping by combining a wake oscillator model with a quasi-steady galloping force in a square column with an aspect ratio of 1.5, which was used to consider the VIV and galloping phenomena in a structure [21]. [PERSON] selected a typical open-section beam based on a prototype of the Aftetal Bridge and studied its unsteady galloping stability through wind tunnel tests [22]. To avoid the occurrence of galloping, which is severely destructive, the possibility of galloping is usually judged according to the Den Hartog criterion in the wind-resistance design of a bridge. So far, many scholars have made some achievements in the stability of galloping vibrations. [PERSON] used the energy analysis method, took a two-dimensional square column as the research object, and used the dynamic mesh technology. The possibility of galloping in the section was studied, and the influences of various vibration frequencies, amplitudes, and wind speeds on the input energy of the aerodynamic force were discussed [23]. Some researchers [24; 25] proposed that the error of the galloping force coefficient is huge when the Den Hartog criterion is used to calculate the galloping vibration of a single-column bridge tower with variable cross sections. [PERSON] and [PERSON] [26; 27; 28] carried out some experimental studies on the galloping stability of a stayed cable, and it was found that the galloping phenomenon of this cable with an asymmetrical cross section was largely affected by the wind attack angle. However, the galloping force coefficient calculated with the Den Hartog criterion was different from that in the measured results. Based on the quasi-steady-state theory, the galloping characteristics of the structure of a bluff body section are influenced by the wind attack angle [29], which can be deduced from the critical wind speed for galloping and the amplitude calculation formula under the influence of the wind attack angle. It can be deduced that only conditions with a wind attack angle of 0\({}^{\circ}\) are considered in [PERSON]'s theory. Based on the quasi-steady-state assumption, there are no clear calculation methods or theories for the galloping criterion with the non-zero degrees of the wind attack angle. Therefore, for a bridge section that may experience quasi-steady galloping at high wind speeds, the [PERSON] criterion may not be fully applicable at any wind attack angle. It is significant to determine the critical galloping wind speed of a bridge with a larger wind attack angle. A formula for the vibration force coefficient that considers the influence of the wind attack angle on galloping, which was proposed by [PERSON] et al. [30], contains multiple derivatives of the tri-component force coefficient. [PERSON] [31] proposed a galloping stability analysis method through a computational fluid dynamics (CFD) simulation, which still needs to be verified with wind tunnel tests, and its calculation accuracy is easily affected by many parameters. In the current research, the traditional galloping criteria are based on the quasi-steady-state assumption, and the classic [PERSON] galloping theory is found to only effectively determine the critical wind speed of galloping when the wind attack angle is less than 25\({}^{\circ}\). However, it is impossible to accurately predict the critical wind speed for galloping under inflow conditions with a large angle of attack. This study takes into account the classic [PERSON] galloping theory and proposes a galloping stability criterion for structures that can consider the influences of different incoming wind attack angles through theoretical analysis. Firstly, by taking a square section as the research object, the variation in the section's galloping force coefficient is analyzed by using three different galloping stability criteria (the dCV/d\(\alpha\) criterion, the [PERSON] criterion, and the Xie criterion).