Unified theory for identifying vertical and radial damping ratios of curved bridges by two connected scanning vehicles

Abstract

A unified theory is presented for identifying the vertical and radial damping ratios of a horizontal curved bridge by the correlation between two connected scanning vehicles using the variational mode decomposition (VMD) and synchrosqueezed wavelet transform (SWT). Firstly, closed-form solutions are derived for the out-of-plane and in-plane responses of the curved beam caused by the gravitational and centrifugal forces, respectively, of the two moving vehicles. Then, generalized contact formulas are presented for calculating the vertical and radial responses of the vehicle-bridge contact points from the vehicle’s responses, to avoid vehicle frequencies’ masking effect. Subsequently, the instantaneous amplitudes of the component responses of the curved bridge are obtained by the VMD-SWT technique. Finally, generalized damping formulas for retrieving the vertical and radial damping ratios of the curved bridge are established by utilizing the spatial correlation between the two vehicles. This paper has demonstrated that: (1) the vertical and radial damping ratios of the curved bridge can be successfully and precisely identified; (2) the generalized damping formula for curved beams has been attested to be robust against various factors; and (3) the adverse effect of road roughness on damping ratio recovery can be mitigated by the aid of accompany traffic.