﻿
 doi:

DOI: 10.3724/SP.J.1249.2018.02128

Journal of Shenzhen University Science and Engineering (深圳大学学报理工版) 2018/35:2 PP.128-131

## Calculation of CQC mode correlation coefficients under filtered white noise model of earthquake ground motion

• WANG Gang 1   ZHOU Xiaoqing 1
• 1.College of Civil Engineering, Shenzhen University, Shenzhen 518060, Guongdong Province, P. R. China

Abstract：
When filtered white noise is used to model ground motion, the computation of complete quadratic combination (CQC) modal correlation coefficients by integration of rational function becomes difficult, and the closed-form formulas become tedious and impractical. We propose a new method to obtain modal correlation coefficients by transforming transfer function model into state space model and then by solving a Lyapunov equation. This method can be extended to the situation where filtered white noise ground motion models are used. Kanai/Tajimi model is used to verify the correctness of the proposed method. It is not only concise, reliable and numerical efficient but also can avoid solving tedious closed-form formulas of integration of rational functions.

Key words：seismic engineering,modal correlation coefficient,complete quadratic combination,mode-superposition response spectrum analysis,Lyapunov equation,filtered white noise

ReleaseDate：2018-03-20 15:26:56

[1] KIUREGHIAN D A. A response spectrum method for random vibration:UCB/EERC-85/15[R]. EERC, Berkeley:University of California, 1980.

[2] KIUREGHIAN A D. A response spectrum method for random vibration analysis of MDF systems[J]. Earthquake Engineering and Structural Dynamics, 1981, 9:419-435.

[3] WILSON E L, BAYO E P. A replacement for the SRSS method in seismic analysis[J]. Earthquake Engineering and Structural Dynamics, 1981, 9(2):187-194.

[4] KIUREGHIAN D A, NAKAMURA Y. CQC modal combination rule for high-frequency modes[J]. Earthquake Engineering and Structural Dynamics, 1993, 22(11):943-956.

[5] POZZI M, KIUREGHIAN D A. Response spectrum analysis for floor acceleration[J]. Earthquake Engineering and Structural Dynamics, 2015, 44(12):2111-2127.

[6] MENUN C, REYES J C, CHOPRA A K. Errors caused by peak factor assumptions in response-spectrum-based analyses[J]. Earthquake Engineering and Structural Dynamics, 2015, 44(12):1729-1746.

[7] NAKAMURA Y. Application of CQC method to seismic response control with viscoelastic dampers. in:gardoni p.(eds) risk and reliability analysis:theory and applications[M]. Springer Series in Reliability Engineering. Cham:Springer, 2017.

[8] 周锡元,马东辉,俞瑞芳.工程结构中的阻尼与复振型地震响应的完全平方组合[J].土木工程学报,2005, 38(1):31-39. ZHOU Xiyuan, MA Donghui, YU Ruifang. Damping in structures and complete quadratic combination (CCQC) of complex mode seismic responses[J]. China Civil Engineering Journal, 2005, 38(1):31-39.(in Chinese)

[9] 王刚,王远,周文松.考虑一阶系统参与组合的复模态分解反应谱法[J].地震工程与工程振动,2013, 33(4):89-94. WANG Gang, WANG Yuan, ZHOU Wensong. Complex modal superposition response spectrum method with first order system entering combination[J]. Earthquake Engineering and Engineering Vibration, 2013, 33(4):89-94.(in Chinese)

[10] KANAI K. Semi-empirical formula for the seismic characteristics of the ground[J]. Bulletin of the Earthquake Research Institute, 1957, 35(2):309-325.

[11] TAJIMI H. A statistical method of determining the maximum response of a building structure during an earthquake[C]//Proceedings of the Second World Conference on Earthquake Engineering, Tokyo and Kyoto, Japan:Science Council of Japan, 1960, 2:781-798.

[12] CLOUGH R W, PENZIEN J. Dynamics of structures[M]. New York:McGraw-Hill,1993.

[13] 欧进萍, 牛荻涛, 杜修力.设计用随机地震动的模型及其参数确定[J].地震工程与工程震动, 1991,11(3):45-54. OU Jinping, NIU Ditao, DU Xiuli. Random earthquake ground motion and its parameter determination used in aseismic design[J]. Earthquake Engineering and Engineering Vibration, 1991,11(3):45-54.(in Chinese)

[14] 洪峰, 江近仁, 李玉亭. 地震地面运动的功率谱模型及其参数的确定[J].地震工程与工程震动, 1994, 14(2):48-54. HONG Feng, JIANG Jinren, LI Yuting. Power spectral models of earthquake motions and evaluation of its parameters[J]. Earthquake Engineering and Engineering Vibration,1994,14(2):48-54.(in Chinese)

[15] 杜修力, 陈厚群. 地震动随机模拟及其参数确定方法[J]. 地震工程与工程振动, 1994, 14(4):1-5. DU Xiuli, CHEN Houqun. Random simulation and its parameter determination method of earthquake ground motion[J]. Earthquake Engineering and Engineering Vibration, 1994,14(4):1-5.(in Chinese)

[16] 李英民,刘立平,赖明. 工程地震动随机功率谱模型的分析与改进[J]. 工程力学,2008,25(3):43-48,57. LI Yingmin, LIU Liping, LAI Ming. Analysis and improvement of power random spectra of strong ground motions for engineering purpose[J]. Engineering Mechanics, 2008,25(3):43-48, 57.(in Chinese)

[17] 韩崇昭. 随机系统概论——分析估计与控制[M].北京:清华大学出版社,2014. HAN Chongzhao. Introduction to stochastic systems:analysis, estimation and control[M]. Beijing:Tsinghua University Press, 2014.(in Chinese)

[18] BARTELS R H, STEWART G W. Solution of the matrix equation AX+XB=C[J]. Communications of the ACM, 1972,15(9):820-826.

[19] GOLUB G H, NASH S, VAN LOAN C F. A Hessenberg-Schur method for the problem AX+XB=C[J]. IEEE Transactions on Automatic Control, 1979, 24(6):909-913.