孙测世, 焦德望, 赵碧航, 谭超. 垂索-辅助索系统的建模与固有特性[J]. 工程力学, 2023, 40(11): 168-178. DOI: 10.6052/j.issn.1000-4750.2022.02.0136
引用本文: 孙测世, 焦德望, 赵碧航, 谭超. 垂索-辅助索系统的建模与固有特性[J]. 工程力学, 2023, 40(11): 168-178. DOI: 10.6052/j.issn.1000-4750.2022.02.0136
SUN Ce-shi, JIAO De-wang, ZHAO Bi-hang, TAN Chao. MODELING AND INHERENT CHARACTERISTICS OF SAGGED-CABLE-CROSSTIE SYSTEM[J]. Engineering Mechanics, 2023, 40(11): 168-178. DOI: 10.6052/j.issn.1000-4750.2022.02.0136
Citation: SUN Ce-shi, JIAO De-wang, ZHAO Bi-hang, TAN Chao. MODELING AND INHERENT CHARACTERISTICS OF SAGGED-CABLE-CROSSTIE SYSTEM[J]. Engineering Mechanics, 2023, 40(11): 168-178. DOI: 10.6052/j.issn.1000-4750.2022.02.0136

垂索-辅助索系统的建模与固有特性

MODELING AND INHERENT CHARACTERISTICS OF SAGGED-CABLE-CROSSTIE SYSTEM

  • 摘要: 辅助索被认为是长索振动控制中一种富有潜力的手段。为研究安装辅助索后系统的固有特性及其随关键参数的变化规律,建立了由N根垂索和M道辅助索组成的索网系统的模型,得到其无量纲运动方程,引入边界条件、连续条件和平衡条件进行求解。将模型退化到双索-辅助索系统,求得其无量纲频率方程。采用数值分析研究了Irvine参数λ2、辅助索刚度和位置、波速比η等关键参数对系统频率和模态的影响。研究表明,当两索参数相同时,垂度仅影响反相频率,故同相振动和反相振动的ω-λ2曲线分别表现为“穿越”(cross-over)现象和“转向”(veering)现象。当λ2为某特定值时,任意辅助索刚度下的一阶反相振动频率均等于一阶同相频率,从而频率曲线均通过第一个“穿越”点。两索参数相同时,增大辅助索刚度仅提高系统反相振动频率,但其增幅不超过1。两索波速不同时,系统所有频率均随波速差异增大而发生往高阶的“跳阶”(jumping)现象,且频率阶次越高“跳阶”次数越多。

     

    Abstract: Crosstie is a promising mean for vibration mitigation of long inclined cables. In order to study the inherent characteristics of the system with crosstie and its variation with key parameters, a model for the sagged-cable-crosstie system composed of N vertical cables and of M crossties was established. The dimensionless equation of motion was obtained and then solved by introducing boundary, continuity, and equilibrium conditions. The general model was reduced to a double-cable-crosstie system, and its dimensionless frequency equation was obtained. The effects of key parameters on the frequencies and modes of the system were studied by numerical analysis, such as Irvine parameter λ2, stiffness and location of crossties, and wave velocity ratio η. The results show that the sag only affects the out-of-phase frequency when the parameters of the two cables are the same, so the ω-λ2 curves of in-phase vibration and out-of-phase vibration show cross-over phenomenon and veering phenomenon, respectively. When λ2 is a certain value, the first order out-of-phase vibration frequency under any crosstie stiffnesses is equal to the first order in-phase frequency, thusly the frequency curves pass through the first cross-over point. If the parameters of the two sagged cables are the same, increasing the stiffness of the crosstie only increases the out-of-phase vibration frequency of the system, but the increase is not more than 1. If the wave velocities of the two sagged cables are different, all the frequencies of the system will be “jumping” to higher orders with the increase of the wave velocity difference, and the higher the frequency order, the more the number of “jumping”.

     

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