Semianalytical Approaches in Moving Load Problems Applied on a Three-Layer Railway Track Model

In this contribution, a new form of semianalytical results related to inertial objects that are traversing longitudinally homogeneous infinite structures, introduced in the author’s previous works, is used to analyze plane models of a railway track composed of a guiding structure in the form of a beam and a supporting structure composed of discrete masses, springs, and dampers. The aim of these analyses is to determine the critical velocities of the moving force and the onset of instability of moving masses or oscillators. Further emphasis is placed on the connection between the lowest critical velocity and the onset of instability and on the dynamic interaction between proximate moving inertial objects. All presented results are obtained semianalytically for dimensionless parameters exploiting integral transforms and contour integration. Regarding the critical velocity of a moving force, it is shown that there can be at most three critical velocities. Other terms such as pseudocritical and false critical velocities are introduced. It turns out that these values are strongly associated with the onset of instability of a single moving mass. Nevertheless, the so-called instability lines can have quite irregular behavior, especially at low damping levels.