# Effects of the Configuration of Trailing Edge on the Flutter of an Elongated Bluff Body
## 1 Introduction
[8] proposed an approximate method to calculate the critical wind speed and frequency of flutter by the analysis of a large number of dynamics and aerodynamics data, which only requires three flutter derivatives (\(H_{1}^{*}\), \(A_{2}^{*}\), and \(A_{3}^{*}\)) or two flutter derivatives (\(H_{1}^{*}\) and \(A_{2}^{*}\)) to perform the calculation, and greatly simplifies the approximate calculation of critical wind speed and frequency of flutter. It is suitable for bridges with the section whose bending-torsion coupling is only affected by the shape of a structural mode or a higher mode, but it cannot completely replace more accurate analysis methods. [PERSON] et al. [9] started by simplifying the coefficients in the third and fourth degree polynomials of \(\omega\), derived from the singular condition of the frequency matrix. Under the quasi-steady assumption, they proposed an approximate formula for calculating the flutter of the aeroelastic system. The critical wind speed of flutter of long-span bridges can be estimated well within the range of bending-torsion coupling, and the calculation result fits well with the results of the wind tunnel test. The rapid and approximate calculation of bridges' flutter stability helps to better understand the mechanism of flutter and represents the first step towards a simple engineering tool, which is also of great significance for speeding up the design process of bridges. Researchers found in wind tunnel tests that when the model has a large wind attack angle, or the bridge's deck cross section is a blunt-body section, there will be no obvious divergent flutter, but large-amplitude and limiting-amplitude vibration, called soft flutter, which is also known as limit cycle flutter (LCF) may occur. Correspondingly, the divergent flutter is called hard flutter [10; 11; 12]. [PERSON] et al. [13] used a fluid-structure-coupling model to numerically simulate the aeroelastic response of the bridge deck and verified it with the theoretical solution of the flutter response of a thin plate. It is proposed that the increase in the wind attack angle makes the bridge deck more prone to LCF; the stable amplitude of LCF has nothing to do with the initial excitation, and the increasing the damping of structure can significantly increase the critical wind speed of LCF of the bridge, but it has little effect on the vibration frequency. [PERSON] et al. [14] analyzed the nonlinear aeroelastic behavior of a typical passivated bridge section (that is, the bridge deck with double-sided guardrails opened) through a series of LCF tests of the Spring-Suspended Sectional Model (SSSM). A model of self-excited nonlinear force suitable for large-amplitude vibration is proposed, and its forecast results are compared with experimental results. The identified aerodynamic parameters further indicate that the mechanism of LCF is due to the negative aerodynamic damping provided by the linear term as the energy source to drive the increase in vibration amplitude and the nonlinear positive aerodynamic damping provided by the third-order angular velocity. In the tested wind speed range, the observed stable LCF amplitude increased linearly with the decrease in wind speed. [PERSON] et al. in 2017 [15] researched the flutter characteristics of streamlined bridge decks by using a comprehensive wind tunnel test and introduced a nonlinear mathematical model to simulate the aeroelastic behavior of nonlinear torsional flutter. It was found that nonlinear aerodynamics are the main source of nonlinear vibration. Based on the instantaneous amplitude and instantaneous frequency calculated by the normalized Hilbert transform, a system identification method was developed to extract linear and nonlinear aerodynamic parameters at the same time. On this basis, [PERSON] et al., in 2019, [16] simulated an LCF process of the bridge based on computational fluid dynamics (CFD) and analyzed the energy input in this process.