## 1 Introduction  
Constantly evolving architecture brought about the development of spatial bar structures. These are architecturally stunning buildings, yet in addition to the static-strength analysis, they require a study of their dynamic response, which is related to their individual characteristics. Modal analysis is a design essential tool because it provides information on the structure dynamic parameters. The most important parameters of modal analysis include frequencies and modes of free vibration, which are obtained after solving the eigenproblem. For structures sensitive to dynamic loads (e.g., wind load, earthquake load, crowd of people, impact), modal analysis makes it possible to adopt appropriate measures aimed at reducing vibration and its harmful effects, such as resonance. The need to account for the effect of dynamic loads in the design is illustrated by the example of the motorcycle speedway stadium in Zielona Gora (Poland). Expert opinion on the facility was provided in [1; 2; 3]. In the author's opinion, if the fans had continued jumping for a little longer during the event, the probability of structural collapse would have been high. The undulating movement of the roof would have led to its collapse onto the stand, and the failure mechanism would have been rapid. It was found that the designer had neglected the effect of dynamic loading and had not checked for the possibility of resonance occurrence. As the investigations showed, the frequency of the roof structure free vibration was about 2.45 Hz, whereas during the events, the facility was subjected to vibrations of 2.2-2.3 Hz. This situation, namely, similar frequency values,caused resonant vibrations. During the measurements, it was observed that the pattern of vibration increased considerably when the fans enjoyed themselves very much. Roof vibration was recorded on video footage, clearly indicating resonant excitations. The situation made it necessary to retune the structure. The aim was to ensure that the lowest frequency of free vibration of the roof structure was much higher than the frequency of forced vibration. Finally, it was decided the retuning should include additional support of the girder by a steel column. Numerical analysis showed that the natural frequency spectrum shifted so that the first resonance frequency was 5.31 Hz. The strengthening produced a \"high tuning\" effect. The dynamic load generated by the crowd of people is also the theme of the work [4]. The research was aimed at determining the most effective bracing system for a typical example of a temporary steel grandstand. Three different bracing systems were analyzed using the five criteria recommended in the literature. The greatest improvement in the behavior of the structure was obtained for the stand equipped with a bracing system, meeting all the proposed criteria. The work [5] consisted in the analysis of the seismic response of 100 m, 200 m, and 300 m lattice domes to horizontal and vertical movement during an earthquake. Time history analysis was used to analyze the seismic response of the truss domes. This paper aimed to study the seismic properties of lattice domes in terms of eigenvalue modes, displacement, and acceleration response. In the paper [6] on the dynamic response of lattice domes, cylindrical shell roofs were investigated. Additionally, a simple acceleration response evaluation method using response amplification factors was delivered. The article [7] discusses the optimal geometry of each of the three different types of single-layer steel domes analyzed under gravity and earthquake loads. For earthquake loads, equivalent static, spectral, and time history analysis (THA) methods were used. The article [8] describes a novel excitation method for experimental modal analysis (EMA) in situ compared to ambient vibration analysis, the so-called operational modal analysis (OMA). The analyses were performed on an eleven-story building in Austin, Texas.