Recovering mode shapes of curved bridges by a scanning vehicle

The contribution of this paper is to recover the vertical and radial mode shapes of curved bridges from the contact responses of a single-axle scanning vehicle using the variational mode decomposition (VMD) and synchrosqueezed wavelet transform (SWT) for the first time. To catch both the vertical and radial vibrations of the curved bridge, the test vehicle is modeled as a three degree-of-freedom (DOF) system involving the vertical, rocking, and lateral (radial) displacements. Firstly, closed-form solutions for the out-of-plane and in-plane vibrations of the curved beam under the vehicle's action are derived. Then, the unified formula is derived for calculating the vertical and radial contact responses of the single-axle test vehicle. Finally, the VMD technique is employed to process the vertical and radial contact responses to obtain the component responses, followed by the SWT to generate the mode shapes. The numerical analysis demonstrated that: (1) the unified formula newly derived is good for both vertical and radial responses; (2) more bridge frequencies can be extracted from the contact than vehicle response; (3) the vertical and radial mode shapes of the curved bridge can be successfully recovered by the proposed combined VMD-SWT technique against various factors; and (4) with the aid of random traffic, the adverse effect of pavement roughness on mode shape recovery is alleviated.