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Nonlinear transverse vibrations of a slightly curved beam with hinged–hinged boundaries subject to axial loads

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Abstract

The investigation of curved structures has attracted more and more attention, and the mainstream research focuses on the characteristics of curved beams subject to transverse loads, while sometimes axial loads are inevitable in engineering practice. Hence, this work aims to investigate the nonlinear vibrations of a curved beam subject to axial loads by developing appropriate modeling and solving methods. In this work, a nonlinear dynamic model of a hinged–hinged slightly curved beam (SCB) with sinusoidal shape subject to axial loads is first established, and the modal hypothesis method is subsequently used to obtain natural frequencies and mode shapes of the SCB subject to axial loads. Thereafter, a procedure to calculate the forced vibration responses of the SCB subject to axial loads is proposed by successively using the Galerkin truncation method, harmonic balance method and pseudo arc-length method. Finally, case studies are carried out to validate the above modeling and solving methods of the SCB subject to axial loads and explore its nonlinear dynamic characteristics. On the one hand, the effectiveness and accuracy of the proposed modeling and solving methods are verified by comparing with the results of finite element analysis. On the other hand, the results of the case studies demonstrate that the initial curvature, axial force, external excitation amplitude and initial configuration of the SCB can significantly affect its nonlinear dynamic characteristics.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11802201, 11972245), the Natural Science Foundation of Tianjin City (Grant No. 21JCQNJC00360), the Aeronautical Science Foundation of China (Grant No. 2020Z009048001), and the Young Elite Scientists Sponsorship Program by Tianjin (Grant No. TJSQNTJ-2020-01).

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Authors and Affiliations

  1. School of Mechanical Engineering, Tianjin University, Tianjin, 300350, China

    Yu-Jia Zhai, Zhi-Sai Ma, Qian Ding & Tao Wang

  2. Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin, 300350, China

    Yu-Jia Zhai, Zhi-Sai Ma, Qian Ding & Tao Wang

  3. China Academy of Launch Vehicle Technology, Beijing, 100076, China

    Xiao-Peng Wang

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  1. Yu-Jia Zhai
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Correspondence to Zhi-Sai Ma.

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Zhai, YJ., Ma, ZS., Ding, Q. et al. Nonlinear transverse vibrations of a slightly curved beam with hinged–hinged boundaries subject to axial loads. Arch Appl Mech 92, 2081–2094 (2022). https://doi.org/10.1007/s00419-022-02162-w

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