Vehicle Scanning Method for Bridges

3Vehicle Scanning of Bridge Frequencies: General Theory

This chapter differs from Chapter 2 in that all modes of vibration of the bridge are included in formulation of the general theory for the dynamic interaction between the moving vehicle and bridge. By assuming the vehicle/bridge mass ratio to be small, approximate but highly accurate closed‐form solutions are obtained for the vertical responses of both the bridge and moving vehicle by the method of modal superposition. For both the bridge and vehicle responses, it is confirmed that rather accurate solutions can be obtained by considering only the first mode. The displacement, velocity, and acceleration of the bridge are governed at different extents by two frequency sets pertaining to the driving frequency of the vehicle and natural frequencies of the bridge. From the spectrum for the bridge displacement, the vehicle speeds can be shown to be associated with some low‐frequency pikes. On the other hand, the vehicle responses are governed by five distinct frequencies that appear as driving frequencies, vehicle frequency, and bridge frequencies with shift. From the vehicle’s acceleration spectrum, the first bridge frequency (with shift) is shown to have rather high visibility and can be easily identified. Potential applications of the present results are also indicated. The materials presented in this chapter are based primarily on the paper by Yang and Lin (2005) with necessary corrections on mathematical derivations and ...