###### Abstract  
This study proposes a novel reduced-order model (ROM), based on the Volterra series, for the aerodynamic force of the bridge deck section. Moreover, the ROM of the aerodynamic force of the streamlined box girder section of the Great Belt East Bridge (GBEB) is identified with computational fluid dynamic (CFD) simulations. Furthermore, an analysis method combining ROM aerodynamic force and Newmark-\(\beta\) integration is established to simulate the aeroelastic responses of the bridge deck section. Finally, the wind-induced vibration responses of the GBEB section are calculated near the flutter critical wind speed based on the Volterra series-based aeroelastic analysis and the fluid-structure interaction (FSI) numerical simulations in ANSYS Fluent, respectively. Moreover, to verify the applicability of the proposed method, the aeroelastic responses of the main deck section with the crash barriers of Lingdingyang Bridge (LDYB) are also simulated via the Volterra model and Newmark-\(\beta\) integration near the flutter critical wind speed. The results show that the first-order truncated Volterra model established in this study can accurately capture the aerodynamic response of the main girder, and the results are in good agreement with those of the CFD numerical simulation under forced vibration. Furthermore, the proposed method combined with ROM aerodynamic force and Newmark-\(\beta\) integration can effectively calculate the FSI of the bridge girder. The numerical results of the flutter critical wind speed and flutter frequency of GBEB and LDYB are consistent with the numerical results by the FSI method based on ANSYS Fluent and the existing numerical and experimental results, respectively. reduced-order model (ROM); Volterra series; streamlined box girder section; wind-induced vibration; flutter critical wind speed +
Footnote †: journal: Applied Sciences  
motions of long-span bridges and the significantly blunted aerodynamic shape of the deck ([PERSON] et al. [3]). The above situation may cause significant flow separation and reattachment around the bridge girder section, leading to apparent nonlinearity of aerodynamics and thus, the inaccuracy of the linear flutter theory ([PERSON] [4]). Due to the nonlinear effects of the aerodynamic force on large-amplitude vibrations or large AOAs, many researchers have proposed different aerodynamic reduced-order models (ROMs) to consider the nonlinear effect of aerodynamic force ([PERSON] [5]; [PERSON] [6]; [PERSON] et al. [7]), such as the harmonic balanced (HB) method, proper orthogonal decomposition (POD) method and Volterra series. [PERSON] et al. [8] utilized the HB method for the first time to model unsteady nonlinear flows in turbomachinery, while [PERSON] [9] utilized the POD method to construct an unsteady aerodynamic and aeroelastic model for two-dimensional isolated airfoils in a compressible flow. However, these methods cannot fully consider the fluid memory effects in the fluid-structure interaction (FSI). The fluid memory indicates that both the historical structural motion and the flow field fluctuations have an impact on the current flow field state ([PERSON] et al. [10]). Therefore, the Volterra series is more suitable for solving the complex interaction between the structure and the flow field in the aeroelastic problem, such as vortex-induced vibrations and flutter. [PERSON] [11] utilized the Volterra series theory to analyze a nonlinear system and proposed its discrete form. The identification of the kernels is a crucial step in constructing the Volterra model. Subsequently, [PERSON] et al. [12] and [PERSON] et al. [13] proposed the impulse response method and the step response method to identify the Volterra kernels, respectively. Later, [PERSON] [14] proposed a multi-input-multi-output (MIMO) identification method, which significantly improved the efficiency of the Volterra kernel identification.