An effective procedure for extracting mode shapes of simply-supported bridges using virtual contact-point responses of two-axle vehicles

Abstract

This paper proposed an effective procedure using virtual contact-point responses to extract mode shapes of a simply-supported bridge. The theoretical closed-form solution of virtual contact-point response using two connected two-axle vehicles is derived based on the vehicle-bridge interaction theory. Variational mode decomposition and band-pass filter (VMD-BPF) method is adopted to decompose the virtual contact-point responses and extract the bridge mode shapes. And a mode shape splicing method is proposed to reduce the influence of vehicle length on the bridge mode shape identification. The accuracy of the identified mode shapes is verified by numerical simulations, indicating that the virtual contact-point responses of the front axle or rear axle in the two-axle vehicle can be used for mode shape extraction. Furthermore, parametric studies such as track irregularity, vehicle speed, and noise are conducted to analyze the parameters that affect the identification accuracy of the mode shapes. The results show that the first four order natural frequencies and corresponding mode shapes of bridges can be well identified by the virtual contact-point responses even when the track irregularity of grade 4 is used. It is also demonstrated that the proposed procedure has a good performance and robustness in extracting the mode frequencies and mode shapes of simply-supported bridges.