## 1 Introduction  
Weight reduction is a basic criterion for the design of railway vehicles in order for them to reach high speeds with the lowest possible energy consumption. By reducing the weight of railway vehicles, vibrations transmitted through the ground and manufacturing costs are also reduced. In addition, the demand of transport service providers to maximize the use of axle loads, which are limited, requires the railway industry to adopt lightweight carbody designs [1; 2]. Reducing the carbody weight involves using lighter materials and changing the mechanical structure. This implicitly leads to a decrease in the structural rigidity of the carbody, respectively, to a decrease in eigenfrequencies. The flexibility of the carbody increases the lighter it is, which favours the excitation of structural vibrations of the carbody. The structural vibrations affect the ride comfort, the vehicle's dynamic performance and shorten its life as a result of fatigue stresses [3]. Although the structural vibrations of the carbody are particularly complex, with numerous global and local forms, the first carbody mode of vertical bending has the greatest influence on ride comfort [4]. The eigenfrequency of the first mode of vertical bending of the carbody is usually found in the frequency interval 6 Hz-12 Hz, an interval in which the human body has a greater sensitivity to vertical vibrations [5; 6; 7]. Ride comfort worsens especially in the middle of the carbody, and, in some situations, there may even be repositioning of the critical points from the point in terms of ride comfort from the extremities of the carbody to its middle [8]. The topic of structural vibrations of flexible carbody has become a topic of interest for researchers around the world, the influence of these vibrations on the dynamic behaviour of the railway vehicle being analysed in several studies [1; 3; 9; 10; 11; 12; 13]. Additionally, the problem of reducing or controlling structural vibrations in order to improve ride comfort has been the subject of numerous research. These researches are based on passive, semi-active and active concepts, and can be grouped according to the following approach: concepts that as their purpose to isolate vibrations and aim to reduce the transmission of excitation to the carbody through the suspension [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25], and concepts that as their purpose the damping of the carbody vibrations [26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36] and which aim to reduce the amplitude of the structural vibrations of the carbody [37; 38]. In general, this research uses results obtained through numerical simulations, the numerical simulation applications being developed based on mechanical models of the vehicle-track system obtained through the simplified representation of the real system. There are few cases in which the validation of the concepts or the effectiveness of the proposed methods for reducing the flexible vibration modes of the carbody of the railway vehicles are validated by the results of the experimental research carried out on special test vehicles in the laboratory (Figure 1) [22; 34] or on the line (Figure 2) [35]. Figure 1: The Shinkansen type test vehicle [22; 34]. A separate category of research is dedicated to the possibilities of reducing the flexible vibrations of the carbody of the high-speed electrical multiple units (EMU). Compared to trains with centralized power, EMU use distributed power technology. Distributed power involves mounting several power equipment under the chassis of the carbody, such as traction transformer, traction converter, and air compressor. In addition to the power equipment, other functional systems and equipment are also mounted under the carbody underframe, such as the braking unit, the waste collection unit, etc.