Nonlinear transverse vibrations of a slightly curved beam with hinged–hinged boundaries subject to axial loads
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...
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| Published in: | Archive of applied mechanics (1991) Vol. 92; no. 7; pp. 2081 - 2094 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.07.2022
Springer Nature B.V |
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| ISSN: | 0939-1533, 1432-0681 |
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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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| AbstractList | 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. |
| Author | Wang, Xiao-Peng Zhai, Yu-Jia Ding, Qian Wang, Tao Ma, Zhi-Sai |
| Author_xml | – sequence: 1 givenname: Yu-Jia surname: Zhai fullname: Zhai, Yu-Jia organization: School of Mechanical Engineering, Tianjin University, Tianjin Key Laboratory of Nonlinear Dynamics and Control – sequence: 2 givenname: Zhi-Sai orcidid: 0000-0003-4380-5127 surname: Ma fullname: Ma, Zhi-Sai email: zhisai.ma@tju.edu.cn organization: School of Mechanical Engineering, Tianjin University, Tianjin Key Laboratory of Nonlinear Dynamics and Control – sequence: 3 givenname: Qian surname: Ding fullname: Ding, Qian organization: School of Mechanical Engineering, Tianjin University, Tianjin Key Laboratory of Nonlinear Dynamics and Control – sequence: 4 givenname: Xiao-Peng surname: Wang fullname: Wang, Xiao-Peng organization: China Academy of Launch Vehicle Technology – sequence: 5 givenname: Tao surname: Wang fullname: Wang, Tao organization: School of Mechanical Engineering, Tianjin University, Tianjin Key Laboratory of Nonlinear Dynamics and Control |
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| CitedBy_id | crossref_primary_10_1016_j_ijmecsci_2024_109365 crossref_primary_10_1007_s42417_025_02080_5 crossref_primary_10_1016_j_engstruct_2024_117444 crossref_primary_10_1007_s11071_024_09440_y crossref_primary_10_1016_j_ijnonlinmec_2022_104259 crossref_primary_10_1016_j_ijnonlinmec_2023_104409 crossref_primary_10_1016_j_jsv_2025_119387 |
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| Keywords | Slightly curved beam Initial curvature Axial loads Initial configuration Nonlinear transverse vibrations |
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| SubjectTerms | Axial forces Axial loads Case studies Classical Mechanics Curved beams Dynamic characteristics Dynamic models Engineering Finite element method Forced vibration Harmonic balance method Modelling Nonlinear dynamics Original Resonant frequencies Theoretical and Applied Mechanics Transverse loads Transverse oscillation Vibration response |
| Title | Nonlinear transverse vibrations of a slightly curved beam with hinged–hinged boundaries subject to axial loads |
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