Investigation of time-varying frequencies of two-axle vehicles and bridges during interaction using drive-by methods and improved multisynchrosqueezing transform

Recent studies have highlighted the superiority of the drive-by method using vehicle responses to identify bridge frequencies due to its cost-effectiveness. However, most research identifies bridge and vehicle frequencies as time-invariant, which neglects the non-stationary nature of vehicle–bridge interaction systems. This assumption holds true only when the vehicle’s mass is significantly less than that of the bridge. With an increase in vehicle–bridge mass ratio, relying on this assumption can lead to substantial errors, necessitating an investigation of time-varying characteristics extracted from vehicle responses. This study extends this exploration to extract time-varying frequencies of a vehicle–bridge interaction system involving a two-axle vehicle and a bridge through the drive-by method and improved multisynchrosqueezing transform. The semi-analytical solution for time-varying frequencies is newly derived, and numerical simulations are employed to verify the solution and the effectiveness of the improved multisynchrosqueezing transform. Various influencing factors, including vehicle speed, vehicle damping, bridge damping, stiffness of the bridge and vehicle, environmental noises, and road roughness, are analyzed. Additionally, laboratory experiments with a scaled two-axle vehicle and two bridge models are conducted to verify the proposed method, and case studies on different parameters are further provided. Results demonstrated that the time-varying bridge frequency can be extracted from vehicle responses using the proposed approach. Finally, a novel index is proposed to evaluate the extraction results of the bridge’s time-varying frequency from vehicle responses.