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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Vydané v:Archive of applied mechanics (1991) Ročník 92; číslo 7; s. 2081 - 2094
Hlavní autori: Zhai, Yu-Jia, Ma, Zhi-Sai, Ding, Qian, Wang, Xiao-Peng, Wang, Tao
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2022
Springer Nature B.V
Predmet:
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
Slightly curved beam
Initial curvature
Axial loads
Initial configuration
Nonlinear transverse vibrations
ISSN:0939-1533, 1432-0681
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Popis
Shrnutí: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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ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-022-02162-w