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<p>This study presents a theoretical framework for analyzing the spatial coupled flexural–torsional vibration of thin-walled beam bridges under moving train loads. The train is modeled as a dual-axle moving load series, representing front and rear wheel subsystems with constant spacing. Based on Vlasov's thin-walled beam theory, the governing equations incorporate warping stiffness, rotational inertia and additional torsional moments induced by changes in the position of the shear center—a mechanism often neglected in prior analyses. Closed-form solutions for lateral and torsional displacements are derived using Fourier and Laplace transforms. Validation against finite element method (FEM) and prior studies confirms the accuracy of the proposed theoretical method. Results show excellent agreement with both finite element simulations and existing reference solutions. Furthermore, various influencing parameters, including additional torsional moments, dual impact of train-to-bridge length ratio and speed, fixed wheelbase of a vehicle-to-inter-car distance ratio (i.e., <i>L</i><sub>c</sub>/<i>L</i><sub>d</sub>) and eccentricity, are systematically analyzed. The maximum dynamic amplification factors (DAFs) obtained when additional torsional moments are considered is 8.82% higher than that calculated without accounting for such effects, which demonstrates that incorporating additional torsional moment effects can significantly improve prediction accuracy. Vibration amplitudes exhibit a non-monotonic, sinusoidal-like trend with speed, peaking at critical vehicle-to-bridge length ratios. With each 1-m increment in fixed wheelbase <i>L</i><sub>c</sub> over the range 17 m to 19 m, the lateral displacement amplitude grows by approximately 6.16%, while the torsional displacement amplitude increases by about 6.6%. Both the lateral and torsional displacement amplitudes exhibit an approximately linear increase as a function of the load eccentricity. These findings provide a theoretical foundation for the dynamic assessment and optimization of thin-walled beam bridges under moving train loads.</p>

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Theoretical method for spatial flexural–torsional vibration of thin-walled beams under moving concentrated load series

  • 期刊论文

  • 发表日期：

    2026年3月5日

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  • Xiaoyong Lv,
  • Zhaofa Luo,
  • Yanchen Pan,
  • Da Wang,
  • Zhiwu Yu,
  • Peng Liu

摘要

This study presents a theoretical framework for analyzing the spatial coupled flexural–torsional vibration of thin-walled beam bridges under moving train loads. The train is modeled as a dual-axle moving load series, representing front and rear wheel subsystems with constant spacing. Based on Vlasov's thin-walled beam theory, the governing equations incorporate warping stiffness, rotational inertia and additional torsional moments induced by changes in the position of the shear center—a mechanism often neglected in prior analyses. Closed-form solutions for lateral and torsional displacements are derived using Fourier and Laplace transforms. Validation against finite element method (FEM) and prior studies confirms the accuracy of the proposed theoretical method. Results show excellent agreement with both finite element simulations and existing reference solutions. Furthermore, various influencing parameters, including additional torsional moments, dual impact of train-to-bridge length ratio and speed, fixed wheelbase of a vehicle-to-inter-car distance ratio (i.e., Lc/Ld) and eccentricity, are systematically analyzed. The maximum dynamic amplification factors (DAFs) obtained when additional torsional moments are considered is 8.82% higher than that calculated without accounting for such effects, which demonstrates that incorporating additional torsional moment effects can significantly improve prediction accuracy. Vibration amplitudes exhibit a non-monotonic, sinusoidal-like trend with speed, peaking at critical vehicle-to-bridge length ratios. With each 1-m increment in fixed wheelbase Lc over the range 17 m to 19 m, the lateral displacement amplitude grows by approximately 6.16%, while the torsional displacement amplitude increases by about 6.6%. Both the lateral and torsional displacement amplitudes exhibit an approximately linear increase as a function of the load eccentricity. These findings provide a theoretical foundation for the dynamic assessment and optimization of thin-walled beam bridges under moving train loads.