Instability of vehicle systems moving along an infinite beam on a viscoelastic foundation

The stability of vibrations of vehicle systems moving along an infinite beam resting on a viscoelastic foundation is studied. Two types of complex vehicle systems are considered according to their specific characteristics. The first one is modeled as a system of three elastically connected elements where two cases of connection between the vehicle elements are considered: the traditional and the one proposed here that includes the allowed transverse displacement. The second type of vehicle is modeled as a mechanical system with primary and secondary suspensions. In both types, identical primary supports are modeled as a system of springs and dashpots attached to the bars on the one side, which interact with the beam through the concentrated masses on the other side. It is assumed that the masses and the beam are always in contact. Stability conditions are determined and discussed for both types of vehicles, along with the important advantages of the proposed couplings in the first type and the effect of the secondary suspension in the second type of the moving vehicle. The paper analyzes the case when the vehicle system exceeds the minimum phase velocity of waves in the beam, which may lead to the vibration of the system making it unstable. The instability regions are found for the complex vehicle system by applying the principle of argument, method of contour integration and D-decomposition method. The main novelties in the paper are the results of the stability of vibrations of the two described models that are considered for the first time using the above procedure and methods. As a technical novelty, the effect of a combination of special viscoelastic couplings between elements that could have beneficial influences on the stability of the moving system is considered. Also, within the parametric stability analysis, the influence of the secondary vehicle suspension on the change of the region of stability for varying velocities is shown.