Metrikine A.V.,
Verichev S.N., Blaauwendraad J.

Stability of a twomass oscillator moving on a beam supported by a viscoelastic halfspace 
International
Journal of Solids and Structures 42, 11871207 (2005) doi:10.1016/j.ijsolstr.2004.03.006 
Summary. This paper presents a theoretical study of the stability of a twomass oscillator that moves along a beam on a viscoelastic halfspace. The oscillator and the beam on the halfspace are employed to model a bogie of a train and a railway track, respectively. Using Laplace and Fourier integral transforms, expressions for the dynamic stiffness of the beam are derived in the point of contact with the oscillator. It is shown that the imaginary part of this stiffness can be negative thereby corresponding to socalled negative damping. This damping can destabilize the oscillator leading to the exponential growth of the oscillator’s displacement. The instability zone corresponding to such behavior is found in the space of the system’s parameters with the help of the Ddecomposition method. A parametric study of this zone is carried out with the emphasis on the effect of the material damping in the halfspace and the viscous damping in the oscillator. It is shown that a proper combination of these damping mechanisms stabilizes the system effectively. An attempt is made to construct a onedimensional foundation of the beam so that the instability zone predicted by the resulting onedimensional model would coincide with that obtained from the original threedimensional model. It is shown that such foundation can be constructed but its parameters are ambiguous and can not be determined apriori, without tuning the instability zone. Therefore, it is concluded that onedimensional models should not be used for the stability analysis of highspeed trains. 