Theoretical study on a dual-beam model for detection of track/bridge frequencies and track modulus by a moving vehicle

A theory is presented for retrieving the track/bridge frequencies and track modulus from an instrumented vehicle moving over a dual-beam model to simulate the track-bridge system. The dual beams are connected by uniform spring-dashpot units to simulate the effects of sleepers and ballast, etc. Based on the dual-beam model, the response of the vehicle is firstly derived in closed form, along with that for the vehicle-track contact point. The dual frequencies solved relate to the track and bridge frequencies. Compared with the vehicle spectrum, the contact-point (CP) spectrum is superior in that it is free of the vehicle and driving frequencies. Using the first plus frequency of the dual-beam system, the track modulus can be computed by a simple formula. The proposed technique is numerically validated against the key parameters involved. It is concluded that: (1) the first plus frequency can be retrieved from the contact-point spectrum as an outstanding peak; (2) track irregularity has an adverse, but tolerable, effect on retrieval of track modulus; (3) as a trade-off between efficiency and accuracy, the vehicle is suggested to move at a moderate speed; and (4) the proposed technique may be affected by track damping, but remains good for tracks with infinite length.

Automated summary

A theory is proposed to retrieve track/bridge frequencies and track modulus using a dual-beam model to simulate the track-bridge system. By analyzing the dual-beam model, the first plus frequency can be found from the contact-point spectrum, allowing for the computation of track modulus.