# Research on an Improved Method for Galloping Stability Analysis Considering Large Angles of Attack
## 1 Introduction  
For a long time, the wind-resistant stability of bridges has attracted wide attention in the wind engineering community. In particular, the galloping of a bridge is a speed-dependent, damping-controlled, single-degree-of-freedom phenomenon of aeroelastic instability and it easily occurs when the aspect ratio of a bluff's body section is small, such as in a main steel girder, a steel bridge tower, cables, box-type arch ribs of long-span steel arch bridges, etc. This is a kind of low-frequency (from 0.25 to 1.25 Hz), high-amplitude (from a few centimeters to 6 m), and self-excited scattered vibration [1]. Therefore, once galloping occurs, it causes serious damage to bridge structures [2]. To study galloping, researchers generally use wind tunnel tests, numerical simulations, and theoretical analysis methods. [PERSON] et al. used a numerical simulation method to simulate the transverse and torsional directions of rectangular sections at different aspect ratios with low Reynolds numbers. The results of the numerical simulation were consistent with the quasi-steady-state analysis theory of galloping [3]. [PERSON] et al. conducted static and dynamic wind tunnel tests to evaluate the galloping stability of a section, and the results showed that the static and dynamic test results were in good agreement [4, 5]. Then, they conducted relevant research on the galloping instability of two-dimensional objects with elliptical cross sections and attempted to establish relationships between differentparameters based on a stability map of the cross sections [6]. [PERSON] studied the phenomenon of galloping with a single degree of freedom in the lateral direction through the quasi-steady-state assumption, analyzed the phenomenon of hysteresis in galloping, and obtained an approximate solution to the model by assuming that the aerodynamic force and damping force were much smaller than the inertial force and stiffness force [7]. [PERSON] et al. proposed the concept of energy harvesting by using the galloping behavior and conducted related research on the galloping behavior of differently shaped sections [8]. It was pointed out that it is necessary to carry out a coupling analysis on a galloping system to study its maximum level of harvested power. In terms of theoretical research, [PERSON] proposed a reduced-order model of lateral galloping, which was composed of a pair of nonlinear Langevin equations, so as to calculate the amplitude and phase of the lateral motion of a blunt body section [9]. Subsequently, by studying a pair of identical parallelly oriented cantilever beams, it was found that standard nonlinear macroscopic structures exhibit steady-state response curves that are considerably different from the universal curve that Parkinson obtained for linear structures [10]. At the same time, some studies considered the complex interactions between vortex-induced vibration (VIV) and galloping, the distribution of trailing-edge vortex shedding between the two, and the limitations of the quasi-steady-state theoretical analysis [11; 12; 13]. [PERSON] et al. proposed a model with an empirical formula to predict the response amplitude of the interaction between VIV and galloping vibration. By comparing typical mathematical models, the key parameters affecting the response amplitude were determined [14]. H-type hangers are widely used in steel truss bridges and arch bridges due to their superior flexural performance [15]. This typical bluff body section is prone to wind-induced vibrations, such as galloping, under wind loads [16; 17; 18]. [PERSON] studied the instability of a 2:1 rectangular column as a result of the interaction of VIV and unsteady galloping, compared the measurement results of forced and free vibration and unsteady galloping forces, and pointed out that forced vibration is not suitable for studying the nonlinear behavior of unsteady galloping forces on blunt bodies [19; 20].