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| 1:1 primary resonance and stability analysis about suspension cable based on modal shapes coupling effect |
| Received:November 23, 2020 Revised:April 28, 2021 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20201123004 |
| KeyWord:three-order modal shapes suspension cable 1:1 primary resonance multiscale method amplitude-frequency equations |
| Author | Institution |
| 闵光云 |
中山大学 中法核技术与工程学院, 珠海 ;重庆交通大学 土木工程学院, 重庆 |
| 刘小会 |
重庆交通大学 省部共建山区桥梁及隧道工程国家重点实验室, 重庆 ;重庆交通大学 土木工程学院, 重庆 |
| 蔡萌琦 |
成都大学 建筑与土木工程学院, 成都 |
| 易航宇 |
重庆交通大学 土木工程学院, 重庆 |
| 孙测世 |
重庆交通大学 省部共建山区桥梁及隧道工程国家重点实验室, 重庆 ;重庆交通大学 土木工程学院, 重庆 |
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| Abstract: |
| Aiming at the vibration of suspension cable,the influences of mode shapes coupling effect on the vibration characteristics of suspension cables are studied.Based on the variational principle for Hamiltonian,the partial differential equations of suspension cables considering the influences of bending stiffness are derived,and the first three-order mode shapes coupled ordinary differential equations of suspension cables are obtained by Galerkin method.The first-order,second-order and third-order primary resonance of the suspension are analyzed by the multiscale method,and then the amplitude-frequency response equations of the first-order,second-order and third-order primary resonances are obtained.Then the stability analysis is also carried out based on the Lyapunov stability theory and the numerical examples are analyzed.The results of the numerical examples show that when the 1:1 primary resonance occurs,the amplitude of the first-order resonance is much larger than that of the second-order and third-order primary resonances;in the same order amplitude-σ curve,the amplitude of 1:1 primary resonance increases with the increases of F;in the amplitude-V curve,the critical jumping point has a right deviation trend with the increase of σ,and the increases of σ would lead to the increase of amplitude;the larger the span length is,the larger the amplitudes of 1:1 primary resonances of the first-order,second-order and third-order are,but the amplitude of the first-order primary resonance increases most obviously. |
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