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Flexural–torsional vibration of thin-walled beams with open cross sections considering the additional torsional moment

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Abstract

This paper proposes a solution for analyzing the flexural–torsional response of a thin-walled beam with an open mono-symmetric cross section and under moving loads induced by a moving mass. The additional torsional moment induced by the variation of the shear center location, lateral forces and rotary inertia are taken into consideration in the governing differential equations of motion. According to the Fourier finite integral transformation, the Laplace–Carson transformations and their inverse transformations, the analytical solutions are acquired for vibrational behaviors of beams. The reliability and advancement of the proposed analytical solutions are confirmed by comparing the analytical results originated from the proposed solution with those calculated by previous solutions in the relative literature. Based on the proposed solutions, an extensive parametric study is conducted to investigate the effect of the influential parameters on dynamic response of thin-walled beams, involving the additional torsional moment, lateral forces, velocities, eccentricities and mass of the moving object. The findings reveal that the additional torsional moment plays an important role in lateral displacements of thin-walled beams, especially for the beams subjected to excitation induced by a heavy mass moving at high velocities. Besides, lateral displacements increase with the rise of the additional torsional moment. It is also suggested that the rise of velocities of a moving mass, lateral forces, or eccentricities result in the growth of lateral displacements of beams.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China, Grant Numbers 51078354.

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Authors and Affiliations

  1. School of Civil Engineering, Central South University, Changsha, 410075, China

    Yong Cai, Haijun Chen & Xiaoyue Fan

  2. School of Civil Engineering, Central South University of Forestry and Technology, Changsha, 410004, China

    Xiaoyong Lv

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  1. Yong Cai
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Cai, Y., Chen, H., Fan, X. et al. Flexural–torsional vibration of thin-walled beams with open cross sections considering the additional torsional moment. Acta Mech 234, 6341–6357 (2023). https://doi.org/10.1007/s00707-023-03719-8

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