Under cyclic moving load action, tensile-dominant structures are prone to crack initiation due to cumulative damage effects. The presence of cracks leads to structural stiffness degradation and nonlinear redistribution of dynamic characteristics, thereby compromising str18uctural integrity and service performance. The current research on the dynamic behavior of cracked structures predominantly focuses on transient analysis through high-fidelity finite element models. However, the existing methodologies encounter two critical limitations: computational inefficiency and a trade-off between model fidelity and practicality. Thus, this study presents an innovative analytical framework to investigate the dynamic response of cracked simply supported beams subjected to moving loads. The proposed methodology conceptualizes the cracked beam as a system composed of multiple interconnected sub-beams, each governed by the Euler–Bernoulli beam theory. At crack locations, massless rotational springs are employed to accurately capture the local flexibility induced by these defects. The transfer matrix method is utilized to derive explicit eigenfunctions for the cracked beam system, thereby facilitating the formulation of coupled vehicle–bridge vibration equations through modal superposition. Subsequently, dynamic response analysis is conducted using the Runge–Kutta numerical integration scheme. Extensive numerical simulations reveal the influence of critical parameters—particularly crack depth and location—on the coupled dynamic behavior of the structure subjected to moving loads. The results indicate that at a constant speed, neither crack depth nor position alters the shape of the beam’s vibration curve. The maximum deflection of beams with a 30% crack in the middle span increases by 14.96% compared to those without cracks. Furthermore, crack migration toward the mid-span results in increased mid-span displacement without changing vibration curve topology. For a constant crack depth ratio (γ_i = 0.3), the progressive migration of the crack position from 0.05 L to 0.5 L leads to a 26.4% increase in the mid-span displacement (from 5.3 mm to 6.7 mm). These findings highlight the efficacy of the proposed method in capturing the complex interactions between moving loads and cracked concrete structures, offering valuable insights for structural health monitoring and assessment.

Viscoelastic dampers, leveraging the synergistic mechanism of viscous dissipation and elastic recovery, simultaneously reduce seismic-induced structural displacement and acceleration responses while offering the advantages of simple construction and ease of installation, which hold broad prospects in both the seismic design of new buildings and the retrofitting of existing structures. This work aims to propose a rapid optimization design method for viscoelastic dampers considering torsional effect for three-dimensional solid structures. First, a full-scale prefabricated assembled viscoelastic damper was developed, and mechanical property tests were conducted under a series of loading conditions. Based on the test results, a genetic algorithm is employed to optimize the design scheme of viscoelastic dampers through co-simulation using MATLAB R2022a and OpenSees. The optimization objectives consider both the inter-story drift ratio and acceleration response of the structure, with particular emphasis on the influence of torsional effects. Given that the proposed optimization scheme accounts for structural dynamic characteristics, building functionality, and the universality of seismic excitations, it serves as a design reference for the optimization analysis of other damped structures.