单人步行荷载模型研究
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摘要
对于大跨轻柔结构,人-结构竖向相互作用较为显著,要准确预测结构人致响应,需建立更加精细的单人步行荷载模型。在单自由度弹簧、质量和阻尼(SMD)模型中,引进包含亚谐分量的内部自激励,建立了更加精细的ASMD模型Ⅱ,并对其进行了实验验证。结果表明:当结构自振频率处于亚谐共振区时,需考虑亚谐分量的影响,其影响随人/结构质量比的增加更显著,忽略亚谐分量会导致计算结果偏小;处于倍频共振区时,不考虑人-结构相互作用的共振响应预测结果偏于保守;相比之下,ASMD模型Ⅱ能更好的预测结构人致竖向动力响应。
For large span lightweight structures,the human-structure vertical interaction is significant,so that a more precise walking load model is needed to predict the human-induced vibration more accurately. An ASMD model Ⅱ which consist of a single degree of freedom spring mass damping(SMD) system and an internal actuator was built and verified by experiments. The results show that when the natural frequency of a structure falls into the sub-harmonic resonance region,the impact of sub harmonic component,should be considered,otherwise,the calculation results will incline to be small.When the natural frequency of the structure falls into the main-harmonic resonance region,a pure moving force model will be conservative in its predictions as it does not consider the interaction between the pedestrian and the moving bridge surface.In contrast,the ASMD model Ⅱ can better predict the human-induced vertical responses of the structure.
For large span lightweight structures,the human-structure vertical interaction is significant,so that a more precise walking load model is needed to predict the human-induced vibration more accurately. An ASMD model Ⅱ which consist of a single degree of freedom spring mass damping(SMD) system and an internal actuator was built and verified by experiments. The results show that when the natural frequency of a structure falls into the sub-harmonic resonance region,the impact of sub harmonic component,should be considered,otherwise,the calculation results will incline to be small.When the natural frequency of the structure falls into the main-harmonic resonance region,a pure moving force model will be conservative in its predictions as it does not consider the interaction between the pedestrian and the moving bridge surface.In contrast,the ASMD model Ⅱ can better predict the human-induced vertical responses of the structure.
引文
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[20]DEY P,SYCHTERZ A,NARASIMHAN S,et al.Performance of pedestrian-Load models through experimental studies on lightweight aluminum bridges[J].Journal of Bridge Engineering,2016,21(8):C4015005.
[2]RACIC V,PAVIC A,BROWNJOHN J.Experimental identification and analytical modelling of human walking forces:Literature review[J].Journal of Sound&Vibration,2009,326(1/2):1-49.
[3]ZˇIVANOVIC'S,PAVIC'A,REYNOLDS P.Probability-based prediction of multi-mode vibration response to walking excitation[J].Engineering Structures,2007,29(6):942-954.
[4]BROWNJOHN J,PAVIC'A,OMENZETTER P.A spectral density approach for modelling continuous vertical forces on pedestrian structures due to walking[J].Canadian Journal of Civil Engineering,2004,31(1):65-77.
[5]谢伟平,何卫,艾康伟.车站结构人行荷载特性研究[J].工程力学,2012,29(12):256-264.XIE Weiping,HE Wei,AI Kangwei.Study on characteristics of pedestrian loads of railway station structures[J].Engineering Mechanics,2012,29(12):256-264.
[6]陈隽,王浩祺,彭怡欣.行走激励的傅里叶级数模型及其参数的实验研究[J].振动与冲击,2014,33(8):11-15.CHEN Jun,WANG Haoqi,PENG Yixin.Experimental investigation on Fourier-series model of walking load and its coefficients[J].Journal of Vibration and Shock,2014,33(8):11-15.
[7]陈隽,彭怡欣,王玲.基于步态分析技术的三向单足落步荷载曲线试验建模[J].土木工程学报,2014,47(3):79-87.CHEN Jun,PENG Yixin,WANG ling.Experimental investigation and mathematical modeling of single footfall load using motion capture technology[J].China Civil Engineering Journal,2014,47(3):79-87.
[8]PAVIC'A,REYNOLDS P,SACHSE R.Human-structure dynamic interaction in civil engineering dynamics:A literature review[J].Shock&Vibration Digest,2003,35(1):1-53.
[9]ARCHBOLD P.Evaluation of novel interactive load models of crowd loading on footbridges[C].Proceeding of 4th Symposium on Bridge and Infrastructure Research in Ireland,2008:35-44.
[10]KIM S,PARK S.Leg stiffness increases with speed to modulate gait frequency and propulsion energy[J].Journal of Biomechanics,2011,44(7):1253-1258.
[11]秦敬伟,杨庆山.基于双足步行模型和反馈机制的人体-结构相互作用[J].建筑结构学报,2014,35(增刊1):18-24.QIN Jingwei,YANG Qingshan.Human-structure interaction based on bipedal walking model and feedback mechanism[J].Journal of Building Structures,2014,35(Sup 1):18-24.
[12]何卫,谢伟平,刘隆.人-板耦合系统动力特性研究[J].工程力学,2013,30(1):295-300.HE Wei,XIE Weiping,LIU Long.Study on dynamic characteristics of human-floor interaction system[J].Engineering Mechanics,2013,30(1):295-300.
[13]谢伟平,鲁伟,何卫.人-板耦合系统动力响应及相互作用研究[J].武汉理工大学学报,2015,37(1):56-62.XIE Weiping,LU Wei,HE Wei.Research on dynamic response and interaction of human-floor coupled system[J].Journal of Wuhan University of Technology,2015,37(1):56-62.
[14]谢旭,钟婧如,张鹤,等.人-桥竖向耦合振动计算方法[J].振动与冲击,2016,35(5):108-114.XIE Xu,ZHONG Jingru,ZHANG He,et al.Calculation method for human-bridge vertically coupled vibration[J].Journal of Vibration and Shock,2016,35(5):108-114.
[15]丁阳,米仓.随机人行激励模型改进及应用[J].振动与冲击,2012,31(20):56-60.DING Yang,MI Cang.Improvement of stochastic walking excitation model and its application[J].Journal of Vibration and Shock,2012,31(20):56-60.
[16]MATSUMOTO Y,GRIFFIN M.Mathematical models for the apparent masses of standing subjects exposed to vertical whole-body vibration[J].Journal of Sound&Vibration,2003,260(3):431-451.
[17]SILVA D,BRITO F,PIMENTEL L.Modeling of crowd load in vertical direction using biodynamic model for pedestrians crossing footbridges[J].Canadian Journal of Civil Engineering,2013,40(12):1196-1204.
[18]聂建国,陈宇,樊健生.步行荷载作用下单跨人行桥振动的均方根加速度反应谱法[J].土木工程学报,2010,43(9):109-116.NIE Jianguo,CHEN Yu,FAN Jiansheng.RMS acceleration response spectrum method for single-span footbridges under pedestrian load[J].China Civil Engineering Journal,2010,43(9):109-116.
[19](■)IVANOVIC'S.Modelling human actions on lightweight structures:experimental and numerical developments[C].Matec Web of Conferences,2015,24:01005.
[20]DEY P,SYCHTERZ A,NARASIMHAN S,et al.Performance of pedestrian-Load models through experimental studies on lightweight aluminum bridges[J].Journal of Bridge Engineering,2016,21(8):C4015005.