# Experimental and Numerical Study on Dynamics of Two Footbridges with Different Shapes of Girders
## 1 Introduction  
Dynamic loads are among the most dangerous and unpredicted threats that can be observed in the case of civil engineering structures [1; 2; 3]. Structural vibrations induced by wind, earthquakes, mining tremors, or behavior of people (human-induced vibrations) may lead to damages of structures or serious effects on the health of the users (e.g., [4; 5; 6; 7; 8]). Relatively light and slender footbridges are among different types of structures which are susceptible to dangerous vibrations under dynamic excitations [9]. The problem especially concerns new structures designed using new construction solutions and materials. This is due to the fact that the vibration frequencies of the modern footbridges are often close to the frequencies which are induced by pedestrians [10; 11; 12; 13; 14; 15; 16; 17; 18]. The well-known examples of footbridges that experienced excessive vibrations during exploitation are the Millenium bridge in London [10; 11; 12], the Solferino bridge in Paris [13; 14], and the Mape Valley Great Suspension Bridge [19]. Fortunately, in most of the cases, vibrations were not related to the ultimate limit state but only to the comfort of the users. For this reason, it was necessary to introduce norms and guidelines to the designing process that will allow estimating the vibration comfort of the footbridges [20; 21; 22; 23]. The French Setra guidelines [24] and the European guidelines \"Human-induced vibration of steelstructures\" (HiVoss) [25] are the examples of the most commonly used guidelines related to the criterion of vibrational comfort at footbridges. In order to provide appropriate comfort conditions, many footbridges are currently equipped with additional damping devices. Among them, the Pedro e Ines footbridge in Coimbra [15; 16], Changi Mezzanine Bridge [26; 27], the Footbridge of VW Autostadt in Wolfsburg [28], and tensegrity Kurilpa footbridge [29] can be mentioned. The commonly used devices suppressing excessive vibrations are tuned mass dampers, liquid dampers [19], viscous dampers [30], and active tendons [31]. In order to assess the behavior of the structure, and the risk of occurrence of excessive vibrations, whether at the design or the operation stage, knowledge of its basic dynamic characteristics is mandatory. These modal quantities are natural frequencies, damping ratios, and mode shapes. They can be determined by experimental tests or estimated through numerical analysis. The experimental tests can be carried out on existing structures. The results obtained during the field tests give the objective knowledge of the dynamic structural behavior. A description of the basic steps to identify dynamic parameters of the structure could be found in [32]. They included the creation of a priori models, vibration testing, post-processing of received data, validation and calibration, and also the utilization of a numerical model in some cases [33]. During the experimental study, two basic methods could be distinguished to find out the modal parameters. The first of them was based on the correlation between input data, excitations; and output data, responses of the structure [34; 35; 36]. The second one, called the operational modal analysis (OMA) or ambient modal analysis, was based solely on output data [37; 38; 39]. There are many methods for the identification of dynamic parameters of structures. The most commonly used are the peak--picking method [39], frequency domain decomposition [40], the random decrement technique [41], frequency--domain direct parameter identification method [42], stochastic subspace identification methods [43], and eigensystem realisation algorithm [44]. A good review of the literature on modal identification techniques can be found in [39; 45; 46]. Furthermore, in the literature [38; 47; 48; 39; 49], a comparison of the dynamic parameters identification carried out by various methods could be found.