General theory for separate scanning of vertical and torsional modal properties of thin-walled girders by a moving four-wheel test vehicle

Abstract

The novelty of this paper is to make full use of the four wheels’ signals of a scanning vehicle in detecting the frequencies, damping ratios, and mode shapes of the bridge. To offer a theoretical basis, closed-form solutions are derived for the responses of a damped mono-symmetric beam. Then, the wheel-bridge contact responses are calculated from those of the vehicle to eliminate the vehicle frequencies’ masking effect. Further, for rigid cross sections, the vertical and torsional-flexural responses of the bridge are separated from those of the left and right wheels. The Gabor transform is employed to convert the responses from time to time-frequency domain. Of interest is the dual role played by the front and rear wheels via their spatial correlation. First, for the wheels acting at the same location, but different instants (due to their time lag), the bridge damping ratio is determined as a measure of the decay in response. Second, for the wheels acting at the same instant, but different locations (spanned by vehicle length), the amplitude ratio of two adjacent modal points is used in recovering the mode shapes that are free of damping distortion. The present method is validated by the finite element simulation with the conclusions: (1) the vertical and torsional frequencies, damping ratios, and mode shapes of the bridge can be successfully identified; (2) the theory is robust with regard to bridge damping, vehicle suspension damping, vehicle speed, vehicle’s eccentricity; and (3) the results identified of the modal parameters are acceptable, even in face of pavement roughness and environment noise if the bridge vibration can be properly elevated.