RESUMEN
In this paper, the interaction of a mass moving uniformly on an infinite beam on a three-layer viscoelastic foundation is analyzed with the objective of determining the lowest velocity at the stability limit, called, in this context, the critical velocity. This issue is important for rail transport and, in particular, for the high-speed train, because the moving mass is the basic model of a vehicle, and the infinite beam on a three-layer viscoelastic foundation is the usual mechanical representation of the railway track. In addition to this, the advantages and disadvantages of the two implemented methods, namely, the semi-analytical approach and the Green's function method, are summarized in terms of computational time, the precision of the obtained results, limitations, and the feasibility of implementation. All results are presented in a dimensionless form to cover a wide range of possible scenarios. Some results may be considered academic, however, results related to a particular railway track are also included. Particular attention is paid to the influence of the damping of materials in the foundation upon the critical velocity of the moving mass. Regarding the semi-analytical approach, it is demonstrated that the critical velocities can be obtained in an exact manner by tracing the branches of the so-called instability lines in the velocity-moving-mass plane. This analysis can be maintained within the real domain. As for the time series, they can be determined by a numerical inverse Laplace transform. Moreover, thanks to the analytical form of the final result in the Fourier domain, each value corresponding to a specific time instant can be obtained directly, that is, without the previous time history. Regarding the Green's function method, this is used to verify a few points delimiting the stable and unstable regions of the moving mass with the help of the D-decomposition approach. Additionally, a numerical algorithm based on the Green's function and convolution integral written for dimensionless quantities is used to calculate the time series of the moving mass. In addition to identifying the critical velocity of the moving mass, its connection with the critical velocity of the moving force is emphasized, and the possibility of validating the results on long finite beams using modal expansion is presented and described.
RESUMEN
The rail pad is the elastic element between the rail and the sleeper that has the role of absorbing the mechanical stresses from the rail and reducing the vibrations and shocks generated by wheel-rail interactions. In this paper, the problem of the influence of the variability of the nonlinear load-deformation characteristic of rail pads (resulting from the manufacturing process) on wheel-rail vibrations is investigated. The limit load-deformation characteristics of a manufactured rail pad and the medium load-deformation characteristic resulting as the arithmetic mean of the two are considered. The nonlinear load-deformation characteristic of the ballast is also considered. All these characteristics are approximated with the help of the bilinear function and are implemented in a track model consisting of an infinite Euler-Bernoulli beam placed on a two-elastic layer continuous foundation with inertial insertion, resulting in a model with an inhomogeneous foundation. The parameters of the inhomogeneous foundation are established from the equilibrium condition under a static load. Wheel-rail vibrations are studied in terms of the contact force and the acceleration of the rail and wheel. The influence of the variability of the elastic characteristics of the rail pad manifests itself in the field of medium frequencies, which amplify or attenuate the vibration levels in certain bands of one-third of an octave.