Moving-load issues in beam dynamics: a decade review

Dynamic vibration induced by moving loads poses a critical challenge for high-speed and heavy-haul bridge engineering. This review systematically synthesizes advances over the past decade, the research paradigm of beam dynamics under moving loads has shifted from conventional single-beam deterministic analysis to multi-beam, multi-vehicle, stochastic and variable-speed coupled nonlinear dynamic analysis, and significant developments have been achieved in beam theories, vehicle–bridge interaction models and solution methods including analytical, numerical and data-driven approaches. However, current research is restricted by three core bottlenecks: mathematical difficulty in deriving unified closed-form solutions, lack of systematic experimental benchmark data, and high computational cost of high-dimensional coupled models. This review proposes an integrated theoretical framework that unifies stochastic track irregularity, time-varying material performance, structural nonlinearity, vibration mitigation, energy harvesting and interpretable artificial intelligence techniques, provides a clear research roadmap for scholars. It offers significant academic reference and engineering implications for advancing bridge dynamics from conventional calculation toward real-time intelligent assessment.