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This paper presents an analytical study of the dynamic responses in the vehicle–pavement–foundation system, where the vehicle is simplified to a two-degree-of-freedom system, the pavement is modeled using both Euler–Bernoulli (E-B) beam and Timoshenko beam with consideration of pavement roughness, and the subgrade is simulated with a Winkler foundation model featuring cubic nonlinear stiffness. The focus is on using approximate analytical solutions of pavement response to discuss the impact of nonlinear stiffness under various parameter conditions. In previous analytical studies of vehicle–pavement–foundation systems, vehicles were typically simplified to a constant moving force, leading to the conclusion that when the applied force is small, the impact of nonlinear stiffness on the pavement's dynamic response is minimal; whereas when the force is large, the pavement response increases with the increase in nonlinear stiffness. In this study, the force exerted by the vehicle on the pavement is harmonic, and the impact of nonlinear stiffness on the pavement response is different and much more complex. The research finds that there is a critical value for nonlinear stiffness under the given vehicle parameter conditions: when the nonlinear stiffness is less than the critical value, it has almost no effect on the pavement response; when it exceeds the critical value, the pavement's response first decreases and then increases with the increase in nonlinear stiffness. The critical value of nonlinear stiffness is not fixed and increases as the vehicle velocity and foundation damping. Moreover, an increase in nonlinear stiffness also causes an increase in the offset between the wheel position and the position of maximum pavement deformation. Under the same parameter conditions, the offset in the E-B beam is significantly greater than that in the Timoshenko beam. Our study's results enhance the understanding of the nonlinear dynamics within the vehicle–pavement interaction. [ABSTRACT FROM AUTHOR]

Cracks, common indicators of deterioration in bridge frameworks, frequently stem from wear and rust, leading to increased local flexibility and changes in the structure's dynamic behavior. This study examines how these cracks affect the dynamics of footbridges when subjected to loads generated by walking individuals. The pedestrian is modeled as a linear oscillator, while the cracked bridge is represented by a simply supported beam following Euler–Bernoulli's theory. The use of the Dirac delta function allows for the precise representation of the localized stiffness reduction at the crack location, facilitating the calculation of analytical expressions for the beam's vibration modes. The research suggests that the presence of cracks minimally affects the bridge's mid-span displacement. However, with a limited depth of cracks, the appearance of cracks notably amplifies the mid-span acceleration amplitude of the bridge, leading to a pronounced concentration of energy at the third natural frequency of the bridge in the acceleration spectrum. As the depth and number of cracks increase, the acceleration amplitude continues to decrease, but the corresponding spectrum remains almost unchanged. The study's outcomes enhance the comprehension of how cracks affect the performance of bridge structures when subjected to loads from pedestrians, offering insights for the monitoring and evaluation of the condition of cracked footbridges. [ABSTRACT FROM AUTHOR]