## 1 Introduction  
Suspension bridges are long, slender and flexible structures which are very sensitive to dynamic actions induced by wind, which potentially cause a variety of instability phenomena. The importance of wind-resistant design for these structures has been highly recognized and has led to many research works and investigations on bridge aerodynamics. Some historical views of long-span bridge aerodynamics are presented in [1,2]. The first studies were addressed on the dynamic of suspended cables, pertinent to suspension bridges but without the inclusion of the stiffening girder, see [PERSON] and [PERSON] [3] and [PERSON] [4]. Since the 1980s, starting with [PERSON] and [PERSON] [5] and [PERSON] et al. [6,7], there has been a large number of studies on the free and forced nonlinear vibrations of suspended cables (see the review of [PERSON], in [8,9]). In particular, some papers investigated wind-induced aeroelastic instabilities, as [10, 11, 12]. After the Tacoma Narrows Bridge failure in 1940, major efforts were made to understand the dynamic of suspension bridge, including the effects of the stiffening girder. [PERSON] [13] modeled the stiffening girder as a flexural beam attached to the elastic cables by inextensible hangers. Additional contributions to the continuum model were made by [PERSON] [14]. [PERSON] [15] extended the approach to include coupled vertical-torsional vibrations and the effects of cross-sectional distortion. [PERSON] and [PERSON] [16] and [PERSON] et al. [17] enriched the linearized continuum model including the effects of shear deformation and rotary inertia of the stiffening girder, by concluding that these effects are relatively small and only affect the higher modes of vibration. More recently, in [18] the classical continuum model for the free linear vertical vibrations of a suspension bridge is re-examined. Remarkable attention has been addressed to the aeroelastic behavior of long-span bridges, and especially to the aeroelastic instability, as galloping (1 d.o.f) or flutter (2 d.o.f. ), which may cause catastrophic effects, like in the famous Tacoma Narrows bridge. The modern era of bridge aeroelasticity was launched by [PERSON] [19]. [PERSON] [20], for the first time, analyzed the bridge flutter behavior by exploiting the [PERSON] theory of thin airfoils, with the potential flow assumption. During the same period, empirical formulas were proposed, based on the bridge structural properties only, to directly obtain the critical flutter wind velocity without involving any consideration of the flow field (e.g., [21]). [PERSON] and his colleagues [22] introduced a semiempirical linearized analysis, referred to as \"unsteady theory\", based on the so-called \"flutter derivatives\", which is nowadays still popular among researchers. In [23], advances in aeroelastic analyses of suspension bridges are described, with focus on the numerical simulations carried out for a long-span suspension bridge, using finite difference and discrete vortex methods. More recently, many linear and nonlinear aeroelastic analyses for cable-supported bridges were developed, e.g., [24; 25; 26; 27; 28]. In [24], a nonlinear aerodynamic force model and associated time domain analysis is performed to predict the aeroelastic response of bridges under turbulent winds. In [25], a numerical method for full-bridge aeroelasticity is presented, based on unsteady cross-sectional wind loads and on the finite-element modeling of the structure. In [26], a fully nonlinear model of suspension bridge is proposed to describe overall three-dimensional motions. Torsional-divergence and flutter are studied by numerical methods, able to tackle the coupled nonlinear partial-differential equations of motion. In [27], after a review of the existing linear and nonlinear analyses, two advanced nonlinear models are introduced to study the aeroelastic effects under smooth/turbulent wind conditions: (a) artificial neural network and, (b) Volterra series-based models.