Assembly Procedure for Elementary Matrices of Train-Track-Bridge Railway System

TL;DR

This paper presents a method for assembling elementary matrices to model the dynamic response of a train-track-bridge railway system, using finite element analysis and the Newmark method for numerical integration.

Contribution

It introduces a novel assembly procedure for elementary matrices in railway system modeling and applies the finite element method with MATLAB implementation for dynamic analysis.

Findings

Validated assembly procedure with literature example

Demonstrated high accuracy of the Newmark method in system response

Developed a MATLAB program for dynamic response analysis

Abstract

The aim of this article is to determine the dynamic response of the railway system composed of train, track and bridge, suggesting a method for assembling the elementary matrices to obtain differential equations of the overall system. The model studied consists of a moving part which is the vehicle modeled by a mass-spring-damper system, and a fixed part made up of the rail and bridge deck, modeled by two Bernoulli beams. The ballast layer of the rail bed is represented by springs and continuous dampers. The motion equations are established using the principle of total stationary potential energy in combination with the finite element method. The Newmark method was used to solve the motion equations, whose coefficients depend on time. It is an explicit numerical integration method with unconditional stability and high accuracy, which does not involve any iterative procedure. The concept of the method is explained herein and applied to the railway system studied. A computer program was developed on MATLAB software to analyze the system's dynamic responses. The assembly procedure presented, and the numerical method used to solve the equations in the time domain have been validated there an illustrated example in literature.