Dynamic stability of vibrations and critical velocity of a complex bogie system moving on a flexibly supported infinity track

The paper studies vibrations of a complex bogie system moving along a high order shear deformable beam on a viscoelastic foundation. The complex bogie system is modeled by elastically connected rigid bars on identical supports. An elastic coupling between the bars is introduced to simulate a rigid or flexible (transverse or/and rotational) connection. Identical supports are modeled as a system of springs and dashpots attached to the bars on 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. A new analytically determined critical velocity of the system is presented. The paper analyzes the case when the complex bogie system exceeds the minimum phase velocity of waves in the beam, which may lead to the vibration of the system becoming unstable. The effect of the elastic coupling between the bars on the stability of the system is also analyzed. The instability regions are found for the complex bogie system by applying the principle of the argument and the D-decomposition method.