Separating and detecting the vertical and torsional mode shapes of thin-walled girders from vehicle's contact responses by wavelet transform

The contribution of this paper is to separate and detect the vertical and torsional-flexural mode shapes of thin-walled girders from the traced contact responses of the two wheels of a single-axle test vehicle. To start, closed-form solutions are derived for the vertical, lateral, and torsional vibrations of a mono-symmetric beam. Next, the two wheels’ contact responses back-calculated from the vehicle's responses are manipulated to yield separately the vertical and torsional responses of the bridge, which are free of vehicle's frequencies. Then, the wavelet transform is employed to recover the respective vertical and torsional mode shapes. The present treatment on mode shape recovery of thin-walled girders is an extension of the previous work on frequency identification. This study indicates that: (1) the vertical and torsional mode can be separated and detected from the respective responses by the wavelet transform with no knowledge of relative shape amplitudes; (2) more modal properties of the bridge can be detected from the contact than vehicle response; (3) the proposed method for mode shape recovery is robust with regard to various factors; and (4) ongoing traffic facilitates the recovery of bridge mode shapes, including the torsional ones, even under pavement roughness.