The use of an instrumental three-dimensional two-axle passing vehicle to identify spatial mode shapes of three-dimensional bridges

Indirect measurements of bridge modal properties using instrumental passing vehicles offer a cost-effective technique for the health monitoring of numerous bridges without disrupting traffic. However, existing studies primarily rely on two-dimensional (2-D) test vehicles and bridges, failing to capture essential 3-D dynamics of real-world systems. This study addresses this gap by providing theoretical insights into the use of an instrumental 3-D two-axle passing vehicle to identify spatial mode shapes of 3-D bridges. Closed-form solutions are first derived for the dynamic responses of a 3-D two-axle vehicle interacting with a 3-D thin-walled simple beam, supported by custom-developed 3-D vehicle-bridge interaction (VBI) elements for finite element validation. A hybrid signal processing approach combining variational mode decomposition (VMD) and continuous wavelet transform (CWT) is then proposed to isolate bridge frequencies and reconstruct spatial mode shapes. Numerical examples are employed to validate the approach, examining the effects of vehicle speed, vehicle damping, and road roughness. Theoretical derivations and finite element simulations confirm that vehicle response spectra contain both vertical flexural and lateral flexural-torsional bridge frequencies. The VMD-CWT method successfully distinguishes these frequencies and retrieves spatial mode shapes, achieving modal assurance criterion values exceeding 0.994 and 0.971 for the first and second modes, respectively. Parametric studies indicate that vehicle speed minimally impacts accuracy, vehicle damping enhances frequency identification but slightly degrades mode shape reconstruction, and road roughness reduces overall precision. This study advances vehicle-based indirect measurement by enabling spatial mode identification of 3-D bridges using practical 3-D two-axle vehicles—an achievement beyond the reach of existing 2-D models.