地震反应分析中Caughey阻尼系数的优化解
详细信息 本馆镜像全文    |  推荐本文 | | 获取馆网全文
摘要
传统方法建立Caughey阻尼矩阵时,存在选择多个合理参考频率及避免负模态阻尼比的问题.为此,基于地震反应谱分析,以结构的峰值位移误差最小为优化目标,将模态阻尼比大于零为约束条件,提出了优化Caughey阻尼系数的约束二次规划方法.然后,以一个直径90米,高15米的穹顶结构为例,说明当不同动力反应的显著贡献模态不同,且相应的固有频率有巨大差异时,有必要采用Caughey阻尼矩阵.同时,分析比较了传统方法和优化方法对结构地震反应误差的影响.计算结果表明:传统方法选择的参考频率忽略了不同模态对动力反应贡献的差别,这导致不同激励下的动力反应的计算精度有很大差别;优化方法可使显著贡献模态的阻尼比合理,对于4阶以上Caughey级数,优化方法的计算误差都小于传统方法.
When the Caughey damping matrix is constructed by traditional method,how to choose reasonable multi-reference frequencies and avoid negative modal damping ratios are challenges.Based on the seismic response spectral analysis,an optimal solution of Caughey damping coefficients is proposed by constrained quadratic programming.In the method,by minimizing the error of structural displacement peak and constraining all modal damping ratios to be greater than zero,the Caughey damping coefficients can be determined directly.Then,a dome structure with 90m-diameter and 15m-height is analyzed to illustrate the necessity of Caughey damping when the significant modes for different responses are different and the associated frequencies can differ significantly.Meanwhile,the traditional method and the optimal method are compared in the effects on structural seismic response errors.Numerical results show that the traditional method ignores the difference in different modal contributions to choose reference frequencies and may cause inconsistent accuracies when a structure is subject to different excitations;the optimal method makes the damping ratios of significant contribution modes reasonable,and the errors of the optimal method are smaller than that of the traditional method for more than 4Caughey series.
引文
[1]GB50011-2010.建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.(GB50011-2010.Code for Seismic Design of Buildings[S].Beijing:China Architecture Industry Press,2010.(in Chinese))
    [2]黄宗明,白绍良,赖明.结构地震反应时程分析中的阻尼问题评述[J].地震工程与工程振动,1996,16(2):95-105.(Huang Z M,Bai S L,Lai M.Review on the damping in earthquake response time-history analysis of structures[J].Earthquake Engineering and Engineering Vibration,1996,16(2):95-105.(in Chinese))
    [3]Wilson E L,Penzien J.Evaluation of orthogonal damping matrices[J].International Journal for Numerical Methods in Engineering,1972,4:5-10.
    [4]Adhikari S.Damping modeling using generalized proportional damping[J].Journal of Sound and Vibration,2006,293(1-2):156-170.
    [5]张善元.框架结构平扭耦联弹塑性地震反应分析的力学模型[J].固体力学学报,1983,4:511-519.(Zhang S Y.A model for elasto-plastic dynamic response analysis of space frame structures taking into consideration horizontal-torsional coupling vibration due to earthquake[J].Chinese Journal of Solid Mechanics,1983,4:511-519.(in Chinese))
    [6]任德斌,赵文婷.大跨钢拱薄壳穹顶结构地震响应分析[J].工程力学,2014,31(s):166-170.(Ren D B,Zhao W T.Analysis on seismic response of long-span arch shell steel dome structure[J].Engineering Mechanics,2014,31(s):166-170.(in Chinese))
    [7]李田.结构时程动力分析中的阻尼取值研究[J].土木工程学报,1997,30(3):68-73.(Li T.A study on damping values applied to the time-history dynamic analysis of structures[J].China Civil Engineering Journal,1997,30(3):68-73.(in Chinese))
    [8]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 M L,Zhang J.Discussion on damping models for seismic response analysis of long-span bridge[J].Journal of Vibration and Shock,2009,28(5):22-26.(in Chinese))
    [9]沈飞,楼梦麟.超高层建筑地震反应分析中高阶振型影响分析[J].工程力学,2012,29(SI):23-28.(Shen F,Lou M L.Influence of high modes of high-rise building on its seismic responses[J].Engineering Mechanics,2012,29(SI):23-28.(in Chinese))
    [10]潘旦光.直接确定Rayleigh阻尼系数的一种优化方法[J].工程力学,2013,30(9):16-21.(Pan D G.An optimization method for the direct determination of Rayleigh damping coefficients[J].Engineering Mechanics,2013,30(9):16-21.(in Chinese))
    [11]董军,邓洪洲,王肇民.结构动力分析阻尼模型研究[J].世界地震工程,2000,16(4):63-69.(Dong J,Deng H Z,Wang Z M.Studies on the damping models for structural dynamic time history analysis[J].World Information on Earthquake Engineering,2000,16(4):63-69.(in Chinese))
    [12]R.克拉夫,J.彭津著.结构动力学(第二版)[M].王光远译.北京:高等教育出版社,2006.(Clough R,Penzien J.Dynamics of Structures(Second edition)[M].Translated by Wang Guangyuan.Beijing:Higher Education Press,2006.(in Chinese))
    [13]Caughey T K,O’Kelly M E J.Classical normal modes in damped linear dynamic systems[J].Transactions of ASME,Journal of Applied Mechanics,1965,32:583-588.
    [14]Enrique Luco J.A note on classical damping matrices[J].Earthquake Engineering and Structural Dynamics,2008,37(4):615-626.
    [15]王燕军,梁治安.最优化基础理论与方法[M].上海:复旦大学出版社,2011.(Wang Y J,Liang Z.Optimization Theory and Method[M].Shanghai:Fudan University Press,2011.(in Chinese))
    [16]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(11):15-20,27.(Pan D G.An optimization solution for Rayleigh damping coefficients in seismic response analysis[J].Engineering Mechanics,2013,30(11):15-20,27.(in Chinese))
    [17]Wilson E L.Three-Dimensional Static and Dynamic Analysis of Structures(Third edition)[M].California:Computers and Structures Inc,2002.

版权所有:© 2023 中国地质图书馆 中国地质调查局地学文献中心