## 1 Introduction
Other works about infinite structures have also implemented the D-decomposition method together with the dynamic Green's function [18; 19; 20; 21] or integral transforms [22; 23]. It is commonly assumed that the mass is in permanent contact with the beam [22; 23]; however, in some works, a contact spring is introduced [18; 20; 19; 21]. The critical velocity of the moving force is then usually not analyzed. A connection with the critical velocity and a different approach to identifying instability by tracing the instability lines is presented in [24; 25]. This approach is also suitable for the problem of two moving proximate masses, where a strong dynamic interaction can significantly alter the onset of instability. Using the mentioned approach, the conditions under which the results can be superposed can also be derived, and cases where the dynamic interaction induces instability at a velocity lower than the lowest critical velocity of the moving force can be identified. Additionally, this approach can be readily extended to moving oscillators. Recent works deal with more complicated moving objects or foundation [26; 27; 28]. Further extensions to large deflections are considered in [29]. The change in stiffness of the Winkler foundation introduced with a smooth variation is analyzed in [30; 31]. A moving force is applied in [30], while a moving oscillator is applied in [31]. A comparison of possible methods for solving similar problems is presented in [32]. When inhomogeneity is considered, the moving element method, successfully applied in [33; 34; 35; 36], or the moving window [37] should also be mentioned, because they are efficient in dealing with such situations. In [36], a computationally efficient and accurate numerical method for the dynamic response of a maglev train passing on an \"infinitely\" long multi-span bridge is proposed. The results are validated against test cases from the literature. A novel model for the dynamic interaction of a beam with its foundation is introduced in [38]. It is shown that the Winkler and Pasternak moduli are not constant but time-dependent, because they are influenced by the beam-foundation interaction. Therefore, they are determined as a part of the solution. The mass that is dynamically activated in the foundation is determined in a similar way. The two-layer model of the railway track is quite popular and has already been used to accomplish several objectives, like, e.g., in [39; 40]. The three-layer model is more realistic, and its applicability to represent full finite element models is dealt with in [41] where the question of the critical velocity of the moving force is also briefly discussed. Among other recent works on layered models, [PERSON] [42] can be mentioned. A very long finite three-layer model is considered in [43]. The modal expansion method is applied to a reduced model to increase computational efficiency. A control volume is used to reduce the computational domain, and the structure is traversed by a multi-body model of the vehicle. Recently, artificial intelligence, machine learning and several other metaheuristic algorithms are gaining popularity and have been successfully implemented in identification of the critical velocity of a railway track [44]. Such an approach is fully justified by the fact that the track corridor includes several track sections, and a separate analysis of each of them would be computationally demanding. However, the present paper is dealing with a much simpler situation where the track section is longitudinally homogeneous, and therefore, it is possible to derive (semi)analytical results where all parameter influences are directly present. Therefore, there is no need to seek help in predictions by metaheuristic approaches. In this paper, the two-layer model is analyzed from a different point of view. The goal is to establish the range of parameters leading to an irregular behavior, where \"irregular\" means \"different than expected\". The model is introduced in Section 2, where three irregular situations are described in detail.