Mathematical Modeling of Metro Train-Induced Vibrations Using Finite Element Method

Sustained economic and social growth in India has put a lot of pressure on existing urban traffic system. To overcome this problem several Indian cities has opted for the elevated and underground metro systems, for example New Delhi, Kolkata, Chennai and Jaipur metro. However, in the existing metro routes, due to movement of underground metro trains, vibration was felt at the nearby structures in the form of rattling of windows and door panels. Taking up the case study of Delhi metro, experimental data collected at the site showed that these vibrations have a frequency range of around 35–40 Hz when the traveling speed of the metro is around 40–50 kmph. Therefore, to address this issue a dynamic computational model for both the track and vehicle was developed with the use of finite element method. The whole system was divided into upper part consisting of vehicle body and the lower part consisting of slab track systems. The vehicle has been modeled as the lumped mass system, and slab track is modeled using finite element technique in which rail and slabs are modeled as two-noded beam element; the rail pads, fasteners and slab-resilient materials are represented by spring and damper elements. The interaction between the two parts was obtained through the forces developed between the wheel and the track, which is described by the nonlinear Hertzian contact theory. The primary cause of the force generation is the irregularity of the rail track profile which is modeled as the stationary ergodic Gaussian random process. The irregularity of the track profile is represented by the American Track Irregularity Power spectral density function of grade level 6 in the present study. The responses generated at the rail and slab are compared with the other models in the existing literature.