FREE VIBRATIONS OF A SHALLOW CABLE WITH TWO VISCOUS DAMPERS
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摘要: 随着斜拉索长度的不断增加，在索近梁端单点安装阻尼器已经难以满足拉索减振的需要。同时，已有研究表明索垂度会减弱索端阻尼器的减振效果。因此，针对超长斜拉索，考虑垂度的影响，分析了斜拉索上两处安装粘滞阻尼器(拉索-双粘滞阻尼器)系统的复模态特性。考虑实际中阻尼器一般安装于近索锚固端位置，推导出了该情况下系统模态阻尼比的近似解析表达式，进行了阻尼器参数对索阻尼的影响分析和优化。结果表明：对于双阻尼器系统，垂度仍对拉索对称振动模态的阻尼比有减弱效果，对反对称振动模态无影响；阻尼器对称安装于索两端时，即使考虑垂度索所获得的最优阻尼相比于安装单个阻尼器时可以提高至2倍，能有效解决单阻尼器提供阻尼不足的问题。双阻尼器同端布置相比于仅安离索端较远的阻尼器时，索单阶最优模态阻尼无提高，但对于同时抑制拉索高、低阶振动具有优势。Abstract: With the continuous increase in the length of stay cables in cable-stayed bridges, a damper installed at a point near the cable-deck end is inadequate for cable vibration control. Meanwhile, previous studies have shown that cable sag effect weakens the damping effect of the damper. Therefore, it studies free vibrations of long cables with viscous dampers installed respectively on two points of a cable (cable-two-damper system) and performs complex modal analysis of the system with the sag effect taken into consideration. Asymptotic formulas for modal damping estimation has been derived considering the fact that each damper is close to one cable end in practice. Parametric studies on damper coefficients and locations are carried out to maximize cable damping. The results show that when a cable is equipped with two dampers, cable sag still has an negative effect on cable modal damping in nearly symmetric modes, but has no effect in nearly antisymmetric modes; When the two dampers are symmetrically installed on a cable near its ends, the total modal damping of the cable is approximately the sum of the contributions from each damper when installed separately. It is also found that the dampers both installed at the same cable end cannot improve the maximal attainable damping for a single mode, which can be achieved by only installing one damper farther from the cable end; however, they can achieve better multimode damping effects in terms of simultaneously suppressing high and low mode vibrations of the cable.
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Key words:
- stay cable /
- cable sag /
- double dampers /
- modal damping /
- parameter optimization
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图 2 不同
$ {\lambda ^2} $ 时系统模态阻尼曲线($ {{{l_1}} \mathord{\left/ {\vphantom {{{l_1}} L}} \right. } L} = 0.02 $ )Figure 2. Damping curves for
$ {{{l_1}} \mathord{\left/ {\vphantom {{{l_1}} L}} \right. } L} = 0.02 $ and varied values of$ {\lambda ^2} $ 
图 3 前五阶模态
$ {\lambda ^2} $ 与最大模态阻尼的关系曲线Figure 3. Dependence of maximum modal damping on the cable sag
图 4 两端安装阻尼器系统一阶模态阻尼曲线
Figure 4. First modal damping curves of cable equipped with two dampers at the opposite cable ends
图 5 同一端安装双阻尼器系统一阶模态阻尼曲线
Figure 5. First modal damping curves of cable equipped with two dampers at the same cable end
图 9 两端安装阻尼器系统模态阻尼曲线
Figure 9. Modal damping curves of cable equipped with two dampers at the opposite cable ends
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