Maxwell阻尼耗能结构非平稳地震响应解析分析

PDF(1771 KB)

振动与冲击 ›› 2016, Vol. 35 ›› Issue (19) : 172-180.

论文

李创第 1 ，李暾 1，尉宵腾 2，葛新广 1，邹万杰 1

作者信息 +

Exact response analysis of energy dissipation structures with Maxwell dampers under non-stationary seismic excitation

Li Chuang-di 1 Li Tun 1 Wei Xiao-teng 2 Ge Xin-guang 1 Zou Wan-jie 1

Author information +

文章历史 +

摘要

对单自由度广义Maxwell和多自由度Maxwell阻尼耗能结构非平稳随机地震响应问题进行了系统研究。首先通过构建单自由度和多自由度耗能结构在原始空间和扩阶空间上的特征值和特征向量的精确对应关系，将耗能结构位移、速度和阻尼器受力的时域响应计算公式用结构原始空间上的特征值和特征向量解析表出；然后针对7种经典均匀调制白噪声地震激励和2种经典均匀调制滤过白噪声地震激励，获得了耗能结构位移、速度和阻尼器受力的非平稳均方响应的解析解，并使耗能结构非平稳响应的解析分析与计算，完全转化为耗能结构在原始空间的特征值和特征向量的解析分析与计算，从而构建了基于耗能结构非扩阶特征值和特征向量分析，获得耗能结构非平稳地震响应解析解的一整套方法。

Abstract

Non-stationary random seismic response of SDOF structure with general Maxwell dampers and MDOF structure with Maxwell dampers are studied systematically. The closed-form exact relationships relating eigenvalue and eigenvector in structural extended state space and original space are established, the exact solutions for displacement and velocity or damper transient response of energy dissipation structures can be expressed by using eigenvalues and eigenvectors in structural original space; Then, as for seven kinds of classical uniformly amplitude modulated white noise seismic excitations and two kinds of classical uniformly amplitude modulated filtered white noise seismic excitations, the exact non-stationary response solutions for displacement and velocity or damper of dissipation structures are obtained, which can be also expressed by using eigenvalues and eigenvectors in structural original space, so the complete analytical methods of exact non-stationary seismic response solutions for dissipation structures with Maxwell dampers based on analysis of eigenvalues and eigenvectors in dissipation structural original space are established.

导出引用

李创第 1,李暾 1，尉宵腾 2，葛新广 1，邹万杰 1. Maxwell阻尼耗能结构非平稳地震响应解析分析[J]. 振动与冲击, 2016, 35(19): 172-180

Li Chuang-di 1 Li Tun 1 Wei Xiao-teng 2 Ge Xin-guang 1 Zou Wan-jie 1. Exact response analysis of energy dissipation structures with Maxwell dampers under non-stationary seismic excitation[J]. Journal of Vibration and Shock, 2016, 35(19): 172-180

参考文献

[1] Soong T T, Dargrush G F. Passive engrgy dissipation systems in structural engineering [M]. England: John Wiley and Ltd,1997.
[2] Christopoulos C, Filiatrult A. Principle of passive supplemental damping and seismic isolation [M]. IUSS Press, Pavia, Italy, 2006.
[3] 周云. 粘弹性阻尼减震结构设计[M]. 武汉：武汉理工大学出版社，2006.
Zhou Yun. Viscoelastic damping structure design [M]. Wuhan: Wuhan University of Technology Press, 2006.
[4] 李创第，邹万杰，葛新广，等. 多自由度一般积分型粘弹性阻尼器减震结构的随机响应与等效阻尼[J]. 工程力学，2013，30(4)：136-145.
Li Chuangdi, Zou Wanjie, Ge Xinguang, et al. Random response and equivalent damping of MDOF dissipation structures with general integral model viscoelastic dampers [J]. Engineering Mechanics, 2013, 30(4): 136-135.
[5] 胡聿贤. 地震工程学（第二版）[M]. 北京：地震出版社，2006.
Hu Yuxian. Earthquake Engineering (Second Edition) [M]. Beijing: Earthquake Press.
[6] Amim A, Ang A H S. Non-stationary stochastic model of earthquake motion [J]. Jouenal of the Engineering Mechanics Division, ASCE, 1968, 94(2): 559-583.
[7] Shinozuka M, Sato Y. Simulation of non-stationary random process [J]. Journal of the Engineering Mechanics Division, ASCE, 1967, 93(1): 11-40.
[8] Iyengar R N, Iyengar K T S R. A non-stationary random process for earthquake accleration [J]. Bulletin of the Seismological Society of America, 1968, 59(3): 1163-1188.
[9] Goto H, Toki K. Structural response to non-stationary random excitation [A]. Proc. Fourth. World Conference on Earthqukae Engineering [C], Santiago, Chile, 1969: 130-144.
[10]Fang T, Zhang T S. Non-stationary mean square response due to uniformly amplitude modulated random excitations [J]. 1995, 182(3): 369-379.
[11]李创第，邹万杰，黄天立，等. 结构在水平与竖向地震同时作用的非平稳响应[J]. 土木工程学报，2005，38(6)：25-34.
Li Chuangdi, Zou Wanjie, Huang Tianli, et al. Non-stationary random response of structures to horizontal-vertical earthquake excitations [J]. China Civil Engineering Journal, 2005, 38(6): 25-34.
[12]Park S W. Analytical modeling of viscoelastic dampers for structural and vibration control [J]. International Journal of Solids and Structures, 2001, 38: 8065-8092.
[13]Chang T S, Singh M P. Mechanical model parameter for viscoelastoc dampers [J]. Journal of Engineering Mechanics, 2009, 135(6): 581-584.
[14]Yamada K. Dynamic charateristics of SDOF structure with Maxwell element [J]. Journal of Engineering Mechanics, 2008, 134(5): 396-404.
[15]Palmeri A, Ricciardelli F. State space formulation for linear viscoelastic system with memory [J]. Journal of Engineering Mechanics, 2003, 129(7): 715-724.
[16]Singh M P, Verma N P. Seismic analysis and design with Maxwell dampers [J]. Journal of Engineering Mechanics, 2003, 129(3): 273-282.
[17]Palmeri A. Correlation cofficients for structures with viscoelastic dampers [J]. Engineering Structures, 2006, 28: 1197-1208.
[18]Qian D, Hansen J S. A time domain substructure synthesis method for viscoelastic structure [J]. Journal of Applied Mechanics, 1995, 62: 407-414.
[19]刘延柱，陈文良，陈立群. 振动力学[M]. 北京：高等教育出版社，1998.
Liu Yanzhu, Chen Wenliang, Chen Liqun. Vibration Mechanics [M]. Beijing: Higher Education Press.
[20]方同，薛璞. 振动理论及应用[M]. 西安：西北工业大学出版社，2000.
Fang Tong, Xu Pu. Vibration Theory and Applications [M]. Xian: Northwestern Polytechnical University Press.