**1. Introduction**

There is a large amount of vehicles passing through in-service bridges every day, while sizable wind blows on the bridge decks. Vibrations caused by the service loads is of great theoretical and practical significance in civil engineering. In this chapter, it follows a list, by no means exhaustive, of research related to this kind engineer problem. To start with, Xu *et al.* [1] have explored the basic dynamics interaction between suspension bridges and the combined effects of intense wind and a single

moving train; however, the interaction between the wind and the train dynamics has been altogether neglected. In this limit the suspension bridge response is dominated by wind force. The coupled dynamic analysis of vehicle and cable-stayed bridge system under turbulent wind has also been recently conducted by Xu and Guo [2] under the other limit of low wind speed. In the same view, the both effects of turbulent wind and moving loads on the brigde response are investigated numerically by Chen and Wu [3]. Another interesting results related to the problem of the dynamics of bridges subjected to the combined dynamic loads of vehicles and wind are presented in Refs. [4–6]. To summarize: from the standpoint of bridge engineering the disturbances, either due to wind (in low or high speed limits), passage of heavy loads (single massive trains or disordered aggregates of smaller freight carriers, result in a complex interaction with the bridge vibrations. However, the elastic properties of the bridges are enhanced by the insertion of bearings (the part ranging between the bridge deck and the piers) as a possible protection against severe earthquakes. For if one wants the bearings to protect the bridge, they should isolate the structure from ground vibrations and/or transfer the load to the foundation [7]. Noticed that the bearings can be constituted by some elastic or viscoelastic material. In the literature, the dynamics analysis of bridges with elastic bearings to moving loads has received limited attention. nevertheless, some authors like Yang *et al.* [8], Zhu and Law [9], Naguleswaran [10] and Abu Hilal and Zibdeh [11] have adressed a very interesting resultats about this subjet. There are investigated the pros, and the cons, of the elastic bearings.

The bearings can also be constituted by some viscoelastic materials (such as elastomer)[12]. Therefore, The viscoelastic property of the materials may be modelled by using the constitutive equation of Kelvin-Voigt type, which contain fractional derivatives of real order. In this Chapter we aim to investigate first the pros, and the cons, of the viscoelastic bearings and second the turbulence effect of the wind actions on the response of beam. To accomplish our goal some methods (analytical [13–15] and numerical [13–16]) are used.
