双向地震作用下弱连接双塔结构Rayleigh阻尼矩阵的建模问题
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摘要
以一双塔式直流电压发生器为例,通过4条地震波水平单向、水平和竖直双向激励下双塔结构地震反应峰值计算结果的对比分析,研究双向地震激励下弱连接双塔结构Rayleigh阻尼矩阵的合理建模方式。研究结果表明:当结构的自振基频远低于输入地震波主要分量的激励频率时,在建立Rayleigh阻尼矩阵过程中应考虑输入地震的频谱特性的影响。在仅有水平单向地震激励时,可选用地震激励水平方向的本体塔架振动第1阶自振频率和水平地震波反应谱的峰值频率作为参数频率用于计算Rayleigh阻尼矩阵中的2个比例系数;当水平和竖直双向地震激励时,2个参数频率的选择涉及因数更为复杂,应综合考虑双塔结构的自振频率和输入地震动的特征频率的不同影响。
Taking a pair of tower DC voltage generators as an example, the comparative analysis of the peak results of seismic response of two tower structures under unidirectional, horizontal and vertical bidirectional excitation of four seismic waves is carried out to study the Rayleigh damping of weakly connected twin tower structures under two-way seismic excitation. Reasonable modeling of the matrix. The results show that when the fundamental frequency of the structure is much lower than the excitation frequency of the main component of the input seismic wave, the influence of the spectral characteristics of the input seismic should be considered in the process of establishing the Rayleigh damping matrix. In the case of only horizontal one-way seismic excitation, the first-order natural vibration frequency of the main tower vibration in the horizontal direction of the seismic excitation and the peak frequency of the horizontal seismic wave response spectrum can be used as the parameter frequency to calculate the two proportional coefficients in the Rayleigh damping matrix. When horizontal and vertical two-way seismic excitation, the selection of two parameter frequencies involves more complicated factors, and the different effects of the natural frequency of the two-tower structure and the characteristic frequency of the input ground motion should be considered.
Taking a pair of tower DC voltage generators as an example, the comparative analysis of the peak results of seismic response of two tower structures under unidirectional, horizontal and vertical bidirectional excitation of four seismic waves is carried out to study the Rayleigh damping of weakly connected twin tower structures under two-way seismic excitation. Reasonable modeling of the matrix. The results show that when the fundamental frequency of the structure is much lower than the excitation frequency of the main component of the input seismic wave, the influence of the spectral characteristics of the input seismic should be considered in the process of establishing the Rayleigh damping matrix. In the case of only horizontal one-way seismic excitation, the first-order natural vibration frequency of the main tower vibration in the horizontal direction of the seismic excitation and the peak frequency of the horizontal seismic wave response spectrum can be used as the parameter frequency to calculate the two proportional coefficients in the Rayleigh damping matrix. When horizontal and vertical two-way seismic excitation, the selection of two parameter frequencies involves more complicated factors, and the different effects of the natural frequency of the two-tower structure and the characteristic frequency of the input ground motion should be considered.
引文
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[7] 董云,楼梦麟.基于结构基频的Rayleigh阻尼系数的优化方法及其讨论[J].湖南大学学报,2014,41(2):8-13.DONG Yun,LOU Menglin.Optimization method of Rayleigh damping coefficient based on structural fundamental frequency and its discussion [J].Journal of Hunan University,2014,41(2):8-13.(in Chinese)
[8] 楼梦麟.长周期动力系统时域分析中的阻尼矩阵.力学与工程{M}.郑州:郑州大学出版社,2016,111-117.LOU Menglin.Damping Matrix in Time Domain Analysis of Long-Periodic Dynamic Systems.Mechanics and Engineering{M}.Zhengzhou:Zhengzhou University Press,2016,111-117.(in Chinese)
[9] 楼梦麟,董云.大型直流电压发生器塔架结构地震反应分析[J].防灾减灾工程学报,2013(1):35-40.LOU Menglin,DONG Yun.Seismic response analysis of large DC voltage generator tower structure[J].Journal of Disaster Prevention and Mitigation Engineering,2013(1):35-40.(in Chinese)
[10] 唐玉,楼梦麟.双塔电压发生器地震反应分析的Rayleigh阻尼矩阵[J].哈尔滨工业大学学报,2015,47(2):67-73.TANG Yu,LOU Menglin.Rayleigh damping matrix for seismic response analysis of two-tower voltage generator[J].Journal of Harbin Institute of Technology,2015,47(2):67-73.(in Chinese)
[11] 吴竞,楼梦麟.关于双塔式直流电压发生器结构输入地震波的讨论[J].结构工程师,2017,33(2):135-142.WU Jing,LOU Menglin.Discussion on the input seismic wave of double-tower DC voltage generator structure[J].Structural Engineer,2017,33(2):135-142.(in Chinese)
[2] CHOPRA A K.Dynamics of Structures[M].New York:Prentice Hall,2006.
[3] 楼梦麟,张静.大跨度拱桥地震反应分析中阻尼模型的讨论[J].振动与冲击,2009,28(5):22-26.LOU Menglin,ZHANG Jing.Discussion on damping model in seismic response analysis of long-span arch bridges [J].Vibration and Shock,2009,28(5):22-26.(in Chinese)
[4] 楼梦麟,隋磊,沈飞.不同阻尼矩阵建模对超高层结构地震反应分析的影响[J].结构工程师,2013,29(1):56-63.LOU Menglin,SUI Lei,SHEN Fei.Influence of different damping matrix modeling on seismic response analysis of super high-rise structures [J].Structural Engineer,2013,29(1):56-63.(in Chinese)
[5] 楼梦麟,邵新刚.深覆盖土层Rayleigh阻尼矩阵建模问题的讨论[J].岩土工程学报,2013,35(7):1272-1279.LOU Menglin,SHAO Xingang.Discussion on modeling of Rayleigh damping matrix in deep overburden soil layer [J].Chinese Journal of Geotechnical Engineering,2013,35(7):1272-1279.(in Chinese)
[6] 潘旦光.地震反应分析中Rayleigh阻尼系数的优化解[J].工程力学,2013,30(4):42-46.PAN Danguang.Optimum solution of Rayleigh damping coefficient in seismic response analysis [J].Engineering Mechanics,2013,30 (4):42-46.(in Chinese)
[7] 董云,楼梦麟.基于结构基频的Rayleigh阻尼系数的优化方法及其讨论[J].湖南大学学报,2014,41(2):8-13.DONG Yun,LOU Menglin.Optimization method of Rayleigh damping coefficient based on structural fundamental frequency and its discussion [J].Journal of Hunan University,2014,41(2):8-13.(in Chinese)
[8] 楼梦麟.长周期动力系统时域分析中的阻尼矩阵.力学与工程{M}.郑州:郑州大学出版社,2016,111-117.LOU Menglin.Damping Matrix in Time Domain Analysis of Long-Periodic Dynamic Systems.Mechanics and Engineering{M}.Zhengzhou:Zhengzhou University Press,2016,111-117.(in Chinese)
[9] 楼梦麟,董云.大型直流电压发生器塔架结构地震反应分析[J].防灾减灾工程学报,2013(1):35-40.LOU Menglin,DONG Yun.Seismic response analysis of large DC voltage generator tower structure[J].Journal of Disaster Prevention and Mitigation Engineering,2013(1):35-40.(in Chinese)
[10] 唐玉,楼梦麟.双塔电压发生器地震反应分析的Rayleigh阻尼矩阵[J].哈尔滨工业大学学报,2015,47(2):67-73.TANG Yu,LOU Menglin.Rayleigh damping matrix for seismic response analysis of two-tower voltage generator[J].Journal of Harbin Institute of Technology,2015,47(2):67-73.(in Chinese)
[11] 吴竞,楼梦麟.关于双塔式直流电压发生器结构输入地震波的讨论[J].结构工程师,2017,33(2):135-142.WU Jing,LOU Menglin.Discussion on the input seismic wave of double-tower DC voltage generator structure[J].Structural Engineer,2017,33(2):135-142.(in Chinese)