Damping coefficient optimization of linear fluid viscous damper for suspension bridge
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摘要: 将悬索桥加劲梁纵向运动简化为若干相互独立的单自由度振动系统, 采用随机振动理论, 利用将地震激励简化为平稳白噪声激励的方法推导了加劲梁纵向运动绝对加速度均方的解析表达式。利用导数求极值的原理, 求出了加劲梁纵向运动绝对加速度均方的最小值及其对应的系统最优阻尼比, 得到了悬索桥线性液体黏滞阻尼器最优阻尼系数的解析表达式, 并以某悬索桥为例, 采用动力时程法进行了参数敏感性分析, 验证了解析表达式的有效性。分析结果表明: 悬索桥线性液体黏滞阻尼器存在理论上的最优阻尼比0.5, 其对应的最优阻尼系数使阻尼器的减震效率达到最大值; 当阻尼比为0.3时, 阻尼器的减震效率达到最优阻尼比的90%;当阻尼比在0.4~0.6之间时, 阻尼器的减震效率基本保持在最优阻尼比的99%。综合考虑地震动强度、阻尼器冲程及造价等因素, 线性液体黏滞阻尼器的最优阻尼系数可在阻尼比为0.4~0.6对应的范围内适当调整。Abstract: The longitudinal vibration of suspension bridge stiffening girder was simplified as some independent single degree of freedom vibration systems. Stochastic vibration theory was used, and earthquake excitation was simplified as stationary white-noise excitation, the analytical expression of absolute acceleration mean square for stiffening girder longitudinal vibration was deduced. According to the principle of derivative extremum, the minimum absolute acceleration mean square and the corresponding system optimum damping ratio were derived, and the analytical expression of optimum damping coefficient for suspension bridge linear fluid viscous damper was got. A suspension bridge was selected as example, parametric sensitivity study was carried out based on dynamic time-historical method, and the reliability of the analytical expression was verified. Analysis result shows that the theoretical optimum damping ratio of suspension bridge linear fluid viscous damper is 0.5, and the efficiency of damper reaches its maximum with the corresponding optimum damping coefficient.When damping ratio is 0.3, damper efficiency is about 90% of optimum damping ratio.When damping ratio is 0.4-0.6, damper efficiency is 99% of optimum damping ratio, so the optimum damping coefficient of linear fluid viscous damper can be adjusted properly in the range according to earthquake intensity, damper stroke and cost.
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表 2 最优阻尼系数
Table 2. Optimum damping coefficient
模态阶次 频率/Hz 振型参与质量/103 kg 最优阻尼系数/(kN·s·m-1) 2 0.122 5 503 4 050 4 0.195 3 398 3 997 6 0.293 2 4 合计 8 051 
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表 3 梁端位移响应对比
Table 3. Contrast of beam-end displacement responses
计算值 梁端位移/mm 误差/% 工况1 工况2 最小值 -279.1 -287.2 2.8 最大值 167.2 167.9 0.4
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表 4 计算工况
Table 4. Calculation conditions
工况 振型阻尼比 阻尼系数/(kN·s·m-1) 1 0.3 4 696 2 0.4 6 374 3 0.5 8 051 4 0.6 9 728 5 0.7 11 406
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