Study on Natural Vibration Characteristics of Cable Network-Damper System

doi:10.12141/j.issn.1000-565X.220631

Abstract

Abstract:

In cable-stayed bridges, multiple stay cables are connected with cross-ties and dampers to form a multilevel cable network-damper system, which can effectively reduce the vibration of stay cables. In order to deeply understand the real dynamic behavior of the system and grasp the interaction law of cross-ties and dampers, this paper proposes a model of multilevel cable network-damper system, which simplifies the cross-ties into linear spring elements, and obtains the complex characteristic equation of the system through theoretical derivation. Next, the natural frequency and damping ratio of each order of the system are solved, and local mode parameter is proposed to characterize the local vibration degree of different modes as well as the energy distribution rules of the system, and, furthermore, auxiliary estimate the vibration consistent of the system. Then, the proposed theoretical formulation is verified by the experiment and finite element simulation. Fnially, the changes of vibration mode, frequency, local mode parameter and damping ratio of the triple-layer cable network-single damper system during the change of cross-ties from flexible to rigid are investigated, and the effects of the cross-tie stiffness and damper position on the damping ratio of the system are analyzed. The results show that the multilevel cable networks-damper system decreases the amplitude of the cables and increases damping ratio of the system; that the stiffness change of the cross-tie and the set of damper at the cable end may both lead to corresponding change of multi-order system mode shape; that the change of anchoring position of the damper at the cable end may also cause individual mode shape change.; that the damping ratio is closely related to the amplitude of the section where the damper is located and to the stiffness change of the cross-tie; and that not all mode damping ratios benefit from the damper set at the cable end. In general, the farther the damper is from the bridge deck at the cable-end anchor point, the more favorable it is for the damper to play; the greater the stiffness of the auxiliary cable, the better the integrity of the vibration system; the higher the frequency, the stronger the mutual constraint between the cables.

Key words: cable network-damper system, vibration control, damping ratio, local vibration characteristics

CLC Number:

U443.38

ZHEN Xiaoxia, LIU Guiyuan, DONG Chunguang, et al. Study on Natural Vibration Characteristics of Cable Network-Damper System[J]. Journal of South China University of Technology(Natural Science Edition), 2023, 51(7): 61-71.

Figures/Tables 15

Fig.1

Fig.2

Fig.3

Fig.4

Table 1

Table 2

Fig.5

Table 3

Fig.6

Fig.7

Fig.8

Fig.9

Table 4

Sixth-order damping ratio of the system with different damper positions"

无量纲辅助索刚度	不同阻尼器位置（ $ε 11$ ）时的6阶阻尼比/%
无量纲辅助索刚度	$ε 11$ =5%	$ε 11$ =7%	$ε 11$ =9%	$ε 11$ =11%
0.1	1.02	1.90	2.98	4.22
1.0	1.02	1.91	3.01	4.29
10.0	1.05	2.05	3.41	5.16
100.0	0.00	3.06	4.93	7.08

Table 4

Fig.10

Fig.11

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数值类型	索号	拉力/kN	各阶次频率/Hz
			1阶		2阶		3阶
			无阻尼	有阻尼	无阻尼	有阻尼	无阻尼	有阻尼
实测值	1号索	11.0	18.19	18.19	23.31	23.07	27.10	26.27
	2号索	15.5	18.19	18.19	23.32	23.07	27.10	26.22
	3号索	20.0	18.19	18.19	23.31	23.07	27.10	26.22
解析值	系统	—	16.87	16.86	21.26	21.27	24.96	24.97
仿真值1	系统	—	16.87	16.86	21.26	21.27	24.96	24.97
仿真值2	系统	—	18.67	18.69	23.83	23.84	27.47	27.47

数值类型	索号	阻尼比/%
数值类型	索号	未设置阻尼器	设置阻尼器
实测值	1号索	0.24	0.58
	2号索	0.24	0.62
	3号索	0.24	0.60
解析值	系统	—	0.38
仿真值1	系统	—	0.38
仿真值2	系统	—	0.40

模态阶次	频率/Hz				设置阻尼器时的阻尼比/%				设置阻尼器时的CLM值				未设置阻尼器时^1）的频率/Hz	未设置阻尼器时的CLM值
模态阶次	k= 10⁷ N/m	k= 10⁶ N/m	k= 10⁵ N/m	k= 10⁴ N/m	k= 10⁷ N/m	k= 10⁶ N/m	k= 10⁵ N/m	k= 10⁴ N/m	k= 10⁷ N/m	k= 10⁶ N/m	k= 10⁵ N/m	k= 10⁴ N/m	未设置阻尼器时^1）的频率/Hz	未设置阻尼器时的CLM值
1	1.258	1.258	1.253	1.229	0.19	0.20	0.25	0.46	0	0.01	0.10	0.50	1.258	0
2	2.426	2.203	1.539	1.310	0.08	0.48	0.24	0.06	0.69	0.32	0.30	0.22	2.415	0.63
3	2.430	2.414	1.847	1.371	1.61	0.00	0.07	0.01	0.82	0.32	0.31	0.33	2.433	0.34
4	2.516	2.418	2.417	2.420	0.00	1.10	1.02	1.02	0.63	0.60	0.63	0.63	2.516	0.63
5	2.554	2.516	2.516	2.516	0.02	0.00	0.00	0.00	0.31	0.63	0.63	0.63	2.554	0.31
6	2.625	2.625	2.625	2.625	0.00	0.00	0.00	0.00	0.63	0.63	0.63	0.63	2.625	0.63
7	3.778	3.768	3.702	3.647	0.52	0.63	1.18	1.41	0.01	0.11	0.51	0.63	3.773	0.01
8	4.853	4.492	3.938	3.797	0.05	0.68	0.19	0.01	0.67	0.25	0.22	0.63	4.831	0.63
9	4.887	4.838	4.128	3.950	2.88	0.00	0.03	0.00	0.86	0.30	0.33	0.63	4.868	0.35
10	5.032	4.850	4.850	4.850	0.00	1.98	1.77	1.76	0.63	0.62	0.63	0.63	5.032	0.63

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