To the question of action on the rods lying on elastic foundation, inertial load with a variable speed of its movement

Igor Ivanchenko,B Yazyev

doi:10.1051/e3sconf/202128101036

Abstract

A method for calculating the rods on elastic foundation under the inertial load action when it moves at a variable speed is proposed. Test problems about a force or load movement with variable speeds along a hinged beam and about the movement with a high-speed railway car deceleration along a track section modeled by a hinged supported beam of great length on an elastic foundation are considered. The selection of the elastic foundation material of the rail track determines the dynamics of the high-speed railway car in different modes of its movement. To construct the methodology, the previously proposed by the author of the article solutions are used: a step-by-step procedure for solving the problems of unsteady dynamics of structures and the method of “nodal accelerations” to take into account the action on structures of a moving inertial load.

Highlights

The tasks of studying the interaction of high-speed rolling stock and railway tracks remain relevant [1,2,3,4,5,6,7,8,9]
At the beginning let us turn to the solution of the classical problem of a load movement along a beam on an elastic foundation with a variable speed, and proceed to the case of a more complex load
We will assume that the initial conditions of the problem are zero, and the parameters determining the position e ho in the system O* X*Y*Z*, moving at the car speed progressively, are counted from their values in static equilibrium, while at the moment of the braking start, a horizontal inertia force is applied to the car body, affecting the vertical dynamics of the car

Summary

Introduction

The tasks of studying the interaction of high-speed rolling stock and railway tracks remain relevant [1,2,3,4,5,6,7,8,9]. Let us construct a system of equations describing the vertical dynamics of the car e ho In this case, we will assume that the initial conditions of the problem are zero, and the parameters determining the position e ho in the system O* X*Y*Z* , moving at the car speed progressively, are counted from their values in static equilibrium, while at the moment of the braking start, a horizontal inertia force is applied to the car body, affecting the vertical dynamics of the car (the longitudinal dynamics of the composition is not considered). Let us select a subsystem of equations corresponding to the sub-vector on the left-hand side q ckj 1/ 2 from (11); further we will express this subsystem with respect to the vector of dynamic additions to the static reactions of the wheels, presenting it in the form:.

Numerical simulation results

Conclusion