Nonlinear vibration of thin-walled box beams incorporating axial displacement, torsion distortion and secondary torsion

Minyao  Tan; Dequan  Guo; Bo  Liu; Yu  Liu

doi:10.59400/sv2531

Nonlinear vibration of thin-walled box beams incorporating axial displacement, torsion distortion and secondary torsion

Minyao Tan
School of Automation, Chengdu University of Information Technology, Chengdu 610225, China
Dequan Guo
School of Automation, Chengdu University of Information Technology, Chengdu 610225, China
Bo Liu
Sichuan Academy of Agricultural Machinery Science, Chengdu 610066, China
Yu Liu
Sichuan Academy of Agricultural Machinery Science, Chengdu 610066, China

Article ID: 2531

DOI: https://doi.org/10.59400/sv2531

Keywords: thin-walled box beam; nonuniform torsion; distortion; nonlinear; vibration

Abstract

In this paper, the boundary element method for nonlinear vibration of thin-walled box beams is established, including axial displacement, torsion, distortion, and quadratic torsion. The thin-walled box girders are subjected to conservative dynamic torsional and warping moments that are arbitrarily distributed or concentrated along the length direction. Its control differential equations and boundary conditions are represented by torsion, distortion, and secondary torsional deformation. Its nonlinear terms show strong coupling. The coupling effects of axial displacement, torsion, distortion, and quadratic torsion deformation are fully considered, and the vibration analysis is carried out, respectively, in the state of buckling or post-buckling. The nonlinear differential algebraic equations can be obtained by using the simulation equation method based on the initial boundary value problem, and solved by using an effective time-discrete scheme. In addition, it is proven by two examples that the nonlinear term has a great influence on the torsional moment and the mode of the thin-walled box girder under free vibration. Large torsional rotations increase the torsional stiffness of the thin-walled box beam, ultimately leading to a higher natural frequency. Although the influence of the distortion moment is not as good as that of the torsion moment, it cannot be ignored. The axial inertia term has an obvious influence on the axial stress.

Published

2025-10-16

How to Cite

Tan, M., Guo, D., Liu, B., & Liu, Y. (2025). Nonlinear vibration of thin-walled box beams incorporating axial displacement, torsion distortion and secondary torsion. Sound & Vibration, 59(5). https://doi.org/10.59400/sv2531

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Vol. 59 No. 5 (2025)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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