The method of determining the locations of reinforcing elements in a composite orthotropic plate undergoing dynamic impact. Part 1. Wave problem

Simulation of the railway under dynamic loading. Part 2. Splicing method of the wave and contact solutions

“…For the modeling of the contact the buffer is used, which can be represented as an elastic, visco-elastic and elastoplastic element. For these three elements the dependencies of the arising contact force in the point of interaction on the rail displacement and on mechanic characteristics of applied materials are determined [2,4,5,6] Since the existence of the buffer is a model representation of the contact area between two bodies, the buffer does not loose the stability during the contact process. At the moment of the contact with the rail, the wheelset exhibits a certain velocity, which vertical component is denoted as V0.…”

“…This paper deals with the development of the method of matching solutions of the wave and the contact problem on the border of the area of contact of the impactor and target. There is a fairly large class of methods for determining the parameters of the behavior of structures and their elements under dynamic load, taking into account the wave phenomena [1], oscillations [2] and different rheological properties of the target material [3][4][5][6]. There are also analytical [7] and numerical [8] methods allowing to solve problems of contact interaction of solids, taking into account their movement [9], various geometric and mechanical properties [10].…”

Modelling of the dynamic contact between a wheel of a moving railway vehicle and rails with evaluation of defects emerging upon their interaction. Part 1. The defects of the rail and models of contact

“…In this case different contact models can be applied for the analysis, i.e., the quasistatic Hertz model, the linear elastic model, two elastoplastic contact models: the Aleksandrov-Kadomtsev model and the Kilchevsky model, the viscoelastic model with an exponential kernel of relaxation, the aggregated model based on the Hertz model and the unloading curve, and the viscoelastic model with the Riemann-Liouville fractional derivatives [5][6][7][8][9][10]. 2) The linear elastic model [7,9,11]…”

“…After the substitution of the expressions for vertical displacement of the top structure of a railway track [8,10] at a given point and local deformation (1) -(7), in equation 8we obtain a nonlinear integro-differential equation for the force of interaction, which can be solved using iterative computational algorithm [2,7,8]. This procedure is mostly often used while representing unknown quantities in the form of expansions in a series of time and spatial coordinates [5,9,12].…”

“…Here for a final solution of the described problem and for acquiring graphical or tabular time dependencies of desired characteristics of the railway track's deformation we use the following relations [7,9,11]: 1 21 2 0 0 1 3 5 3 2 1 2 1 0 1 1 4 3 cos 2 cos cos , 2 6 120…”