Boundary Condition and Equivalent Mass-Spring-Damper System for a Truncated Railway Track

To deal with vehicle/track interaction in the time domain, the infinitely long railway track often has to be truncated, generating a finite track model. The ends of the rail in the model are normally simply supported. To account for high-frequency vibration, high train speed and the presence of multiple carriages, the track model must be long, demanding too much computational effort. Means is required to shorten the track model. Aiming at this, the track is divided into three parts, a left semi-infinite part, a middle part (the track model) and a right semi-infinite part. The left and right parts are assumed to be two semi-infinite periodic tracks. The semi-infinite periodic track is replaced with an equivalent mass-spring-damper system. The mass-spring-damper system is determined in such a way that it provides the same receptance to the track model as the semi-infinite periodic track. The receptance of the semi-infinite periodic track is calculated from the response of the two semi-infinite periodic tracks joined together as an infinite periodic structure subject to specific harmonic loads.