Nonlinear vibration analysis of beam-like bridges with multiple breathing cracks under moving vehicle load

The beam-like bridges with small and medium spans are designed to mainly sustain the moving vehicle. Hence, the dynamic behavior of bridges under vehicular loading can provide important information for the bridge design, assessment, and maintenance. Cracks, as one of the most common damage in the bridge structures, alter the bridge dynamic characteristics and therefore responses to the moving vehicle. This paper proposes a novel semi-analytical approach for nonlinear vibration analysis of the beam-like bridges with breathing cracks subjected to vehicular loading, taking into account the dynamic interactions between the vehicle and cracked bridge. The Dirac's delta function is utilized to represent the local stiffness change at the crack location, leading to closed-form solutions of mode shapes of the cracked beam. The breathing process of the crack, causing eigenproperties of the beam to change over time, is characterized by the time -varying curvature of the bridge. Subsequently, the nonlinear dynamic equation of the vehicle -cracked bridge interaction system is established, which is solved through a formulated double -iterative numerical scheme. Eigenvalues and dynamic responses of the bridge with open crack presented in the literature are compared with those obtained from the proposed approach for purposes of validation. The effects of various crack parameters, vehicle speed, and bridge surface irregularity are investigated through a parametric study. In addition, the detection of breathing cracks is also discussed. The results show that the proposed approach can be used to effectively obtain the nonlinear vibration characteristics and dynamic responses of the beam-like bridge with general boundary conditions and different crack numbers, locations, depths, and initial status under moving vehicle. Moreover, the approach has the potential to be incorporated into the vibration-based bridge damage detection.

Automated summary

This paper proposes a novel semi-analytical approach for nonlinear vibration analysis of beam-like bridges with breathing cracks subjected to vehicular loading. The dynamic interactions between the vehicle and cracked bridge are taken into account. The approach utilizes the Dirac's delta function to represent the local stiffness change at the crack location and obtains closed-form solutions of mode shapes. The nonlinear dynamic equation of the vehicle-cracked bridge interaction system is established and solved through a double-iterative numerical scheme. The proposed approach is validated by comparing the results with those from the literature and is shown to effectively obtain the nonlinear vibration characteristics and dynamic responses of the beam-like bridge with different crack parameters, vehicle speeds, and bridge surface irregularities.