Instability of an oscillator moving along a Timoshenko beam on viscoelastic foundation

The paper herein presents an analysis of the vibration instability phenomenon of a three-mass oscillator that is uniformly moving along a continuously viscoelastic supported Timoshenko beam, due to the anomalous Doppler waves excited in the beam. Such phenomenon may appear in the case of railway trains crossing areas with soft soil when the train velocity exceeds the phase velocity of the waves induced in the track structure. The model proposed here corresponds to a two-level suspension vehicle running on a track and it includes the wheel/rail contact nonlinearities (the Hertzian contact characteristic and the possibility of contact loss). First, the velocities at the stability limit are calculated by means of the D-decomposition method via a new form of the characteristic equation based on the receptances; the characteristic equation has been obtained using the Green’s function of the differential operator of the Laplace transformed equations of motion. Therefore, the stability map including two stability/instability zones has been determined. Secondly, the time-domain analysis of the dynamic behavior due to the stability loss has been performed by solving the equations of motion in virtue of the convolution theorem. The previously determined velocities at the stability limit have been confirmed via the time-domain analysis applied to the linear approximation of the equations of motion. Thirdly, the limit cycle characterizing the unstable motion is analyzed. This takes the form of successive shocks, exhibiting a very high magnitude of the contact force, especially in the case of the velocities within the second unstable zone.