多索-单梁耦合结构的动力学建模及非线性特性研究
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湖南省自然科学基金资助项目(2019JJ40534)


Study on dynamic characteristics and nonlinear characteristics of multi-cable single beam coupled structures
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    摘要:

    大跨度斜拉桥通常采用密索体系,拉索的振动频率非常接近,同时拉索之间也可能存在倍频关系.因此,可能存在索与索之间的相互耦合振动.索是斜拉桥的重要承重构件,对多索单梁的动力学特性进行研究至关重要.本文考虑到索梁、索塔及塔梁的边界条件和连接点处的连接条件,基于Hamilton变分原理,建立了多索单梁结构的运动微分方程.经过无量纲化处理,根据分离变量法,得到了其降维约化后的运动微分方程.本文取相邻的两根索考虑两种工况模型,对不同工况下的双索单梁耦合结构的动力学行为进行了参数分析.研究发现,不同于以往资料中的“频率转向”现象,在本文中,两条频率曲线在频率值接近处,并未迅速分离,而是在相对一小段参数范围内继续保持平行且相互靠近,随后再迅速分离.最后,研究了双索单梁耦合结构的非线性特性,分别对结构进行了两自由度和单自由度离散,研究发现,结构单模态假设在非共振区域能反映结构的非线性特性,但是在共振区域,结构的非线性特性会发生跳跃变化,应用2自由度模态理论进行研究更为准确.

    Abstract:

    Long span cable-stayed bridges usually use dense cable systems, and the vibration frequencies of cables are very close, and there may be a frequency doubling relationship between cables. Therefore, there may be mutual coupling vibration between cables. Cable is an important load-bearing component of cablestayed bridges, and it is very important to study the dynamic characteristics of multi cable single beam. In this paper, considering the boundary conditions of cable girder, cable tower and tower girder and the connection conditions at the connection points, based on Hamilton variational principle, the differential equations of motion of multi cable single beam structures are established. After dimensionless treatment, the reduced differential equation of motion is obtained according to the method of separating variables. In this paper, two adjacent cables are taken into account to analyze the dynamic behavior of double cable single beam coupling structure under different working conditions. It is found that, different from the "frequency turn" phenomenon in previous data, in this paper, the two frequency curves do not separate rapidly at the place where the frequency values are close, but continue to keep parallel and close to each other within a relatively small parameter range, and then separate rapidly. Finally, the nonlinear characteristics of the double cable single beam coupling structure are studied, and the structure is discretized with two degrees of freedom and one degree of freedom respectively. It is found that the single mode assumption of the structure can reflect the nonlinear characteristics of the structure in the non resonant region, but in the resonant region, the nonlinear characteristics of the structure will jump, so it is more accurate to apply the two degree of freedom mode theory to research.

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王志搴.多索-单梁耦合结构的动力学建模及非线性特性研究[J].动力学与控制学报,2023,21(4):41~47; Wang Zhiqian. Study on dynamic characteristics and nonlinear characteristics of multi-cable single beam coupled structures[J]. Journal of Dynamics and Control,2023,21(4):41-47.

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  • 收稿日期:2022-10-09
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  • 在线发布日期: 2023-04-20
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