为提高已有绝对位移直接求解虚拟激励法的求解效率及精度，对结构支座节点附加大质量块并释放支座约束，采用基于附加振型的振型分解法进行求解，附加振型来源于附加大质量块。对附加振型、常规振型的振型特性和振型贡献及计算效率进行了理论分析，分析表明：通过构建少量附加振型就可精确捕获结构拟静位移，且只需采用与相对运动法同等数量的常规振型就可精确捕获结构动态相对位移，与Wilson位移输入模式的绝对位移振型分解法相比，在保证计算精度的条件下可大大减少绝对位移求解所需的振型数。此外，对附加振型绝对位移求解法阻尼误差进行了理论分析，指出了附加振型法不存在由于阻尼假定不同而引起的误差，计算精度及效率均优于基于完全法的绝对位移直接求解法。
Abstract
The structures were solved by mode decomposition with additional mode by adding big mass in support nodes, in order to improve the calculation accuracy and efficiency of last pseudo excitation method based on solving absolute displacement. The additional modes are caused by adding big mass. The contribution and characterizes of additional and normal modes and calculation efficiency of new algorithm were analyzed. It is shown that only few additional modes can capture pseudo-static displacement response accurately, and adopting same numbers normal modes with relative motion method can capture same accurate dynamic relative displacement response. Compared with displacement input model presented by Wilson, the method can result in a significant savings in combination mode numbers in the same accuracy. The calculation errors caused by damping assuming difference don’t exist in the new algorithm, which is superior to old pseudo excitation method based on solving absolute displacement in accuracy and efficiency.
关键词
附加振型 /
虚拟激励法 /
绝对位移直接求解 /
振型分解 /
误差分析
{{custom_keyword}} /
Key words
additional modes /
pseudo excitation method /
direct solving absolute displacement method /
mode decomposition /
error analysis
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] 李永华，李思明. 绝对位移直接求解的虚拟激励法[J]. 振动与冲击, 2009, 28(10): 185-190.
LI YONG-HUA, LI SI-MING. Pseudo excitation method based on solving absolute displacement [J]. Journal of Vibration and Shock, 2009, 28(10): 185-190
[2] 张婷, 陈清军, 杨永胜. 两种改进虚拟激励法比较及大跨结构的行波效应分析[J]. 力学季刊，2012, 33(4):612-619
ZHANG TING, CHEN QING-JUN, YANG YONG-SHENG. Comparison between two improved pseudo-excitation methods and analysis of long-span structural traveling waves effects. [J]. Chinese Quarterly of Mechanics，2012, 33(4): 612-619
[3] 赵银庆. 基于虚拟激励的车体结构随机疲劳问题研究[D].大连:大连理工大学, 2010
[4] 贾宏宇，郑史雄. 直接求解多维多点地震动方程的虚拟激励法[J]. 工程力学, 2013, 30(3):341-346.
JIA HONG-YU, ZHENG SHI-XIONG. Pseudo excitation method of direct solving ground motion equation of multi-dimensional and multi-support excitation. [J]. Engineering Mechanics, 2013, 30(3):341-346.
[5] WILSON E L. Static and dynamic analysis of structures: A physical approach with emphasis on earthquake engineering [M]. Berkley, California: Computers and Structures, Inc, 2004.
[6] 胡聿贤. 地震工程学[M]. 北京:地震出版社, 1988.
[7] 李永华，桂国庆.相对运动法与绝对位移直接求解法算法误差分析[J]. 土木建筑与环境工程, 2011, 33(5):83-89
LI YONG-HUA, GUI GUO-QING. Error analysis between relative motion solving method and absolute displacement direct solving method[J]. Journal of Civil, Architectural & Environmental Engineering , 2011, 33(5):83-89
[8] 李永华, 卓平山, 胡远辉. 多点激励下绝对位移直接求解算法的误差频域分析[J]. 振动与冲击, 2012, 31(12): 112-119.
LI YONG-HUA, ZHUO PING-SHAN, HU YUAN-HUI. Error analysis of seismic response obtained by directly solving absolute displacement in frequency domain under multi-support earthquake excitations[J]. Journal of Vibration and Shock, 2012, 31(12): 112-119.
[9] 张林, 高翠琢, 吴景峰. 基于大质量法的谐响应有限元分析[J]. 半导体技术, 2011, 36(5): 402-405
ZHANG LIN, GAO CUI-ZHUO, WU JINGFENG. Harmonic finite element analysis based on large mass method[J]. Semiconductor Technology, 2011, 36(5): 402- 405
[10] 林家浩, 张亚辉. 随机振动的虚拟激励法[M]. 北京:科学出版社, 2004.
[11] 徐培福，傅学怡，王翠坤. 复杂高层建筑结构设计[M]. 北京：中国建筑工业出版社，2005
[12] 俞载道. 结构动力学基础[M]. 上海:同济大学出版社, 1987.
[13] 同济大学数学教研室. 线性代数[M]. 上海:高等教育出版社, 1996.
[14] 石永久,江 洋,王元清.直接求解法在结构多点输入地震响应计算中的应用与改进[J].工程力学, 2011, 28(1): 75-81.
SHI YONG-JIU, JIANG YANG, WANG YUAN-QING. Application and improvement of direct solving method in seismic response analysis of structures under multi-support excitations [J]. Engineering Mechanics, 2011, 28(1): 75-81.
[15] 丰定国，王社良. 抗震结构设计[M]. 武汉:武汉工业大学出版社, 2001.
[16] 赵光恒. 结构动力学[M]. 北京:中国水利水电出版社, 1993.
[17] 周海峰. 行波地震作用下大跨度弦支穹顶结构动力稳定性分析[D]. 南昌: 南昌大学, 2012
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(3351 KB)
