振型降阶法解决被动控制中小刚度引起的病态问题
|
摘要
被动控制系统调谐质量阻尼器(Tuned Mass Damper,TMD)或调谐液体阻尼器(Tuned Liquid Damper,TLD)刚度相对主体结构非常小,而且通常是非线性的,所以动力时程计算中极易出现病态刚度矩阵。当主体结构未知量个数相当大时,刚度矩阵的病态很难避免。为了使病态方程得到改善,本文利用主体结构振型叠加法降低方程阶数。在完成降阶后,根据Newmark-β法推导了计算地震作用下每一时刻结构响应的公式,并将整个算法使用MATLAB编译为程序。通过与已有文献中ABAQUS模拟结果的对比,得出误差在2.9%～8.4%范围内,说明本算法可以提高计算效率,具有较高的精确度。
The stiffness of a passive control system, e.g. Tuned Mass Damper(TMD) or Tuned Liquid Damper(TLD), is very small and nonlinear, which often causes the stiffness matrix to be ill-condition state in dynamic analysis. This illness could rarely be avoided if the number of unknown quantity of main body structure is large. A method is presented in this paper by using mode-superposition method to reduce the number of equations to improve the illness. After the completion of the reduction order, according to the basic principle of Newmark-β method, the formula for calculating the response of each moment under the action of earthquake is deduced, and the whole algorithm is compiled into MATLAB software. By comparing with the results by ABAQUS simulation reported in the previous literature, this algorithm can improve the computational efficiency and has high accuracy. The error rate is about in 2.9%～8.4%.
The stiffness of a passive control system, e.g. Tuned Mass Damper(TMD) or Tuned Liquid Damper(TLD), is very small and nonlinear, which often causes the stiffness matrix to be ill-condition state in dynamic analysis. This illness could rarely be avoided if the number of unknown quantity of main body structure is large. A method is presented in this paper by using mode-superposition method to reduce the number of equations to improve the illness. After the completion of the reduction order, according to the basic principle of Newmark-β method, the formula for calculating the response of each moment under the action of earthquake is deduced, and the whole algorithm is compiled into MATLAB software. By comparing with the results by ABAQUS simulation reported in the previous literature, this algorithm can improve the computational efficiency and has high accuracy. The error rate is about in 2.9%～8.4%.
引文
[1]张国军,张宇鑫,SPENCER B F.调谐质量阻尼器减震控制的研究发展趋势[J].上海师范大学学报(自然科学版),2017,46(2):269-277.(ZHANG Guojun,ZHANG Yuxin,SPENCER B F.Research and development trend of damping control of tuning mass damper[J].Journal of Shanghai normal university(natural science edition),2017,46(2):269-277(in Chinese)).
[2]刘立平,李英民,韩军,等.调液阻尼器减振效应研究的综述和展望[J].土木建筑与环境工程,2006,28(4):132-137.(LIU Liping,LI Yingmin,HAN Jun,et al.Review of current research on the reducing vibration action with tuned liquid damper[J].Civil architecture and environmental engineering,2006,28(4):132-137(in Chinese)).
[3]李宏男,李忠献,祈皑.结构振动与控制[M].北京:中国建筑工业出版社,2005:209.(LI Hongnan,LI Zhongxian,QI Ai.Structural vibration control[M].Beijing:Chinese Building Industry Press,2005:209(in Chinese)).
[4]李庆扬,王能超,易大义.数值分析[M].第5版.北京:清华大学出版社,2008:8-13.(LI Qingyang,WANG Nengchao,YI Dayi.Numerical analysis[M].5th ed.Beijing:Tsinghua University Press,2008:8-13(in Chinese)).
[5]HOUSNER G W.The dynamic behavior of water tanks[J].Bull of the seismological society of America,1963,53(2):381-387.
[6]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(9):16-21.(PAN Danguang.On optimization method for the direct determination of Rayleigh damping coefficients[J].Engineering mechanics,2013(9):16-21(in Chinese)).
[7]李晓雷,俞德孚,孙逢春.机械振动基础[M].北京:北京理工大学出版社,2009.(LI Xiaolei,YU Defu,SUN Fengchun.Fundamentals of mechanical vibration[M].Beijing:Beijing Institute of Technology Press,2009(in Chinese)).
[8]党发宁,殷静,李志宏.克服岩土工程有限元病态问题方法的对比与研究[J].岩石力学与工程学报,2006,25(10):1969-1974.(DANGFaning,YIN Jing,LI Zhihong.Comparison and study of methods for solving finite element ill-conditioned problems in geotechnical engineering[J].Chinese journal of rock mechanics and engineering,2006,25(10):1969-1974(in Chinese)).
[9]胡节良.奇异矩阵的非奇异化处理[J].江西广播电视大学学报,1999,16(1):57-60.(HU Jieliang.The non-singularity treatment of singular matrix[J].Journal of Jiangxi radio and TV university,1999,16(1):57-60(in Chinese)).
[10]克拉夫,彭津.结构动力学[M].北京:科学出版社,1981:134-139.(CLOUGH R W,PENG Jin.Structural dynamics[M].Beijing:Science Press,1981:134-139(in Chinese)).
[11]中华人民共和国住房和城乡建设部.建筑抗震设计规范:GB50011-2010[S].北京:中国建筑工业出版社,2010.(Ministry of Housing and Urban-Rural Construction of the People’s Republic of China.Code for seismic design of buildings:GB50011-2010[S].Beijing:China Architecture Industry Press,2010(in Chinese)).
[12]陈华霆,谭平,和雪峰,等.振型叠加法合理振型数目的确定[J].应用力学学报,2017,34(3):404-409,603.(CHEN Huating,TANPing,HE Xuefeng,et al.Determination of reasonable mode number for mode superposition approach[J].Chinese journal of applied mechanics,2017,34(3):404-409,603(in Chinese)).
[13]苏佶智.矩形调频液体阻尼器三维作用研究[D].包头:内蒙古科技大学,2015:25-35.(SU Jizhi.Research on rectangular tuned liquid damper for three-dimensional vibration reduction[D].Baotou:Inner Mongolia University of Science and Technology,2015:25-35(in Chinese)).
[14]方明霁.高层结构线弹性及弹塑性地震反应分析[D].大连:大连理工大学,2002.(FANG Mingji.Analysis of the elastic and elastic-plastic seismic response of high-rise structures[D].Dalian:Dalian University of Technology,2002(in Chinese)).
[15]NOVO T,VARUM H,TEIXEIRA-DIAS F,et al.Tuned liquid dampers simulation for earthquake response control of buildings[J].Bull of earthquake engineering,2014,12(2):1007-1024.
[16]WOOD W L,BOSSAK M,ZIENKIEWICZ O C.An Alpha modification of Newmark’s method[J].International journal for numerical methods in engineering,2010,15(10):1562-1566.
[17]郁磊.MATLAB智能算法30个案例分析[M].第2版.北京:北京航空航天大学出版社,2015.(YU Lei.MATLAB intelligent algorithms 30 case studies[M].2nd ed.Beijing:Beihang University Press,2015(in Chinese)).
[2]刘立平,李英民,韩军,等.调液阻尼器减振效应研究的综述和展望[J].土木建筑与环境工程,2006,28(4):132-137.(LIU Liping,LI Yingmin,HAN Jun,et al.Review of current research on the reducing vibration action with tuned liquid damper[J].Civil architecture and environmental engineering,2006,28(4):132-137(in Chinese)).
[3]李宏男,李忠献,祈皑.结构振动与控制[M].北京:中国建筑工业出版社,2005:209.(LI Hongnan,LI Zhongxian,QI Ai.Structural vibration control[M].Beijing:Chinese Building Industry Press,2005:209(in Chinese)).
[4]李庆扬,王能超,易大义.数值分析[M].第5版.北京:清华大学出版社,2008:8-13.(LI Qingyang,WANG Nengchao,YI Dayi.Numerical analysis[M].5th ed.Beijing:Tsinghua University Press,2008:8-13(in Chinese)).
[5]HOUSNER G W.The dynamic behavior of water tanks[J].Bull of the seismological society of America,1963,53(2):381-387.
[6]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(9):16-21.(PAN Danguang.On optimization method for the direct determination of Rayleigh damping coefficients[J].Engineering mechanics,2013(9):16-21(in Chinese)).
[7]李晓雷,俞德孚,孙逢春.机械振动基础[M].北京:北京理工大学出版社,2009.(LI Xiaolei,YU Defu,SUN Fengchun.Fundamentals of mechanical vibration[M].Beijing:Beijing Institute of Technology Press,2009(in Chinese)).
[8]党发宁,殷静,李志宏.克服岩土工程有限元病态问题方法的对比与研究[J].岩石力学与工程学报,2006,25(10):1969-1974.(DANGFaning,YIN Jing,LI Zhihong.Comparison and study of methods for solving finite element ill-conditioned problems in geotechnical engineering[J].Chinese journal of rock mechanics and engineering,2006,25(10):1969-1974(in Chinese)).
[9]胡节良.奇异矩阵的非奇异化处理[J].江西广播电视大学学报,1999,16(1):57-60.(HU Jieliang.The non-singularity treatment of singular matrix[J].Journal of Jiangxi radio and TV university,1999,16(1):57-60(in Chinese)).
[10]克拉夫,彭津.结构动力学[M].北京:科学出版社,1981:134-139.(CLOUGH R W,PENG Jin.Structural dynamics[M].Beijing:Science Press,1981:134-139(in Chinese)).
[11]中华人民共和国住房和城乡建设部.建筑抗震设计规范:GB50011-2010[S].北京:中国建筑工业出版社,2010.(Ministry of Housing and Urban-Rural Construction of the People’s Republic of China.Code for seismic design of buildings:GB50011-2010[S].Beijing:China Architecture Industry Press,2010(in Chinese)).
[12]陈华霆,谭平,和雪峰,等.振型叠加法合理振型数目的确定[J].应用力学学报,2017,34(3):404-409,603.(CHEN Huating,TANPing,HE Xuefeng,et al.Determination of reasonable mode number for mode superposition approach[J].Chinese journal of applied mechanics,2017,34(3):404-409,603(in Chinese)).
[13]苏佶智.矩形调频液体阻尼器三维作用研究[D].包头:内蒙古科技大学,2015:25-35.(SU Jizhi.Research on rectangular tuned liquid damper for three-dimensional vibration reduction[D].Baotou:Inner Mongolia University of Science and Technology,2015:25-35(in Chinese)).
[14]方明霁.高层结构线弹性及弹塑性地震反应分析[D].大连:大连理工大学,2002.(FANG Mingji.Analysis of the elastic and elastic-plastic seismic response of high-rise structures[D].Dalian:Dalian University of Technology,2002(in Chinese)).
[15]NOVO T,VARUM H,TEIXEIRA-DIAS F,et al.Tuned liquid dampers simulation for earthquake response control of buildings[J].Bull of earthquake engineering,2014,12(2):1007-1024.
[16]WOOD W L,BOSSAK M,ZIENKIEWICZ O C.An Alpha modification of Newmark’s method[J].International journal for numerical methods in engineering,2010,15(10):1562-1566.
[17]郁磊.MATLAB智能算法30个案例分析[M].第2版.北京:北京航空航天大学出版社,2015.(YU Lei.MATLAB intelligent algorithms 30 case studies[M].2nd ed.Beijing:Beihang University Press,2015(in Chinese)).
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |