多点非均匀调制演变随机激励下结构地震响应
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摘要
针对大跨度结构在非均匀调制演变随机激励作用下，考虑行波效应时的非平稳随机地震 响应问题，应用虚拟激励法进行了分析．由于虚拟激励法自动计及了参振振型的互相关项以及 激励之间的互相关项，理论上是精确解．时变功率谱的计算采用精细逐步积分格式，使计算效 率进一步得到提高．
Prestley's mathematical model of non-uniformly modulated evolutionary random pro- cess takes into account the non-stationary chaxacteristics not only of the excitation intensity, but also of the excitation frequency components. Therefore, it has been considered as physically rather reasonable in simulating general earthquake excitations for a long time. Unfortunately, as this model is expressed in terms of Riemann-Stielties Integration, the relevant computation is very difficult. So far, this model is still considered as unacceptable by practicing engineers even for single excitation problems. In order to simplify the computation, usually the non-stationary characteristics of the excitation frequency components is ignored, namely, the excitations are assumed to be uniformly modulated. In fact, the problem thus simplified is still rather difficult. In this paper, long span structures subjected to non-uniformly modulated differential evolutionary random seismic excitations are analyzed by means of the PEM (pseudo excitation method), an accurate and efficient way. By using this method, the wave passage effect is strictly dealt with, and the cross-correlation terms both between all participant modes and between ground excitations are accurately involved. This method is convenient because the non-stationary random excitations are transformed into deterministic excitations, and so ordinary step-by-step intergration methods such as Newmark or Wilson-0 schemes can be directly used. In this paper) the precise integration method is used, and so the computation efficiency has been further remarkbly raised. A numerical example about an earth-stone dam built in China is given. Its finite element model has about 3000 degrees of freedom and more than 100 ground joints. The results show that it is significant for structural components, which are sensitive to higher frequencies, to regard the excitations as non-uniformly modulated evolutionary random process. It can also be seen that the seismic-wave speed has a considerable influence on structural responses, which are caused by the pseudo-static displacement components.
Prestley's mathematical model of non-uniformly modulated evolutionary random pro- cess takes into account the non-stationary chaxacteristics not only of the excitation intensity, but also of the excitation frequency components. Therefore, it has been considered as physically rather reasonable in simulating general earthquake excitations for a long time. Unfortunately, as this model is expressed in terms of Riemann-Stielties Integration, the relevant computation is very difficult. So far, this model is still considered as unacceptable by practicing engineers even for single excitation problems. In order to simplify the computation, usually the non-stationary characteristics of the excitation frequency components is ignored, namely, the excitations are assumed to be uniformly modulated. In fact, the problem thus simplified is still rather difficult. In this paper, long span structures subjected to non-uniformly modulated differential evolutionary random seismic excitations are analyzed by means of the PEM (pseudo excitation method), an accurate and efficient way. By using this method, the wave passage effect is strictly dealt with, and the cross-correlation terms both between all participant modes and between ground excitations are accurately involved. This method is convenient because the non-stationary random excitations are transformed into deterministic excitations, and so ordinary step-by-step intergration methods such as Newmark or Wilson-0 schemes can be directly used. In this paper) the precise integration method is used, and so the computation efficiency has been further remarkbly raised. A numerical example about an earth-stone dam built in China is given. Its finite element model has about 3000 degrees of freedom and more than 100 ground joints. The results show that it is significant for structural components, which are sensitive to higher frequencies, to regard the excitations as non-uniformly modulated evolutionary random process. It can also be seen that the seismic-wave speed has a considerable influence on structural responses, which are caused by the pseudo-static displacement components.
引文
1 Priestley MB. Power spectral analysis of nonstationary random processes. Journal of Sound and Vibration,1967, 6: 86-97
2 To CWS. Response statistics of discretized structures to non-stationary random processes. Journal of Soundand Vibration, 1986, 106: 217-231
3 Gasparini DA, Debchaudhury A. Response of MDOF systems to filtered non-stationary random excitation. JEgg Mech, ASCE, 1980, 106: 1233-1248
4 Perotti F. Structural response to non-stationary multi-support random excitation. Earthquake Engineering andStrvctural Dynamics. 1990. 19: 513-527
5王君杰,周晶.地震动频谱非平稳性对结构非线性反应的影响.地展工程与工程振动, 1997, 17(2): 16～20(WangJunjie, Zhou Jing. Effects of frequency nonstationarity of seismic ground motion on inelastic response ofstructure. Earthquake Enqineerinq and Engineering Vibration, 1997, 17(2): 16-20 (in Chinese))
6林家浩,张亚辉,孙东科等.受非均匀调制演变随机激励结构响应快速精确算法.计算力学学报, 1997,14(1): 2～8(LinJiahao, Zhang Yahui, Sun Dongke et al. Fast and precise computation of Structural responses to non-uniformlymodulated evolutionary random excitations. Chinese Journal of Computational Mechanica, 1997, 14(1): 2-8(in Chinese))
7林家浩.随机地震响应的确定性算法.地震工程与工程振动, 1985, 5(1): 89～94(Lin Jiahao. A deterministicalgorithm for stochastic seismic response. Earthquake Engineering cud Bngineering Vibrntion, 1985, 5(1):89-94 (in Chinese))
8 Lin Jiahao, Williams FW, Zhang Wenshou. A new approach to multiphase excitation stochastic seismic response.Microcomputers in Civil Engineering, 1993, 8: 283-290
9林家浩,李建俊,张文首.结构受多点非平稳随机地震激励的响应.力学学报,1995,27(5):567～576(Lin Jiahao,LiJianjun, Zhang Wenshou. Structural responses to nonstationary multi-point random seismic excitations. ActaMechanics Sinica, 1995, 27(5): 567-576 (in Chinese))
10 Lin Jiahao, Williams FW. Computation and analysis of multi-excitation random seismic responses. EngineeringComputotions, 1992, 9: 561-574
11 Kiureghian AD, Neuenhofer A. Response spectrum method for multi-support seismic excitations. EarthquakeEngineering and Structural Dynamics, 1989, 21: 713-740
12 Ernesto HZ, Vanmarcke EH. Seismic random vibration analysis of multi-support structural systems. J EggMech, ASCE, 1994, 120(5): 1107-1128
13钟万勰.结构动力方程的精纲时程积分方法.大连理工大学学报, 1994, 34(2): 131～136(Zhong Wanxie. Precisetime integration method for structural dynamic equations. Journal of Dalian University of Technology, 1994,34(2): 131-136 (in Chinese))
14 Lin Jiahao, Shen Weiping, Williams FW. A high precision direct integration scheme for structures subjected totransient dynamic loading. Computers and Structures, 1994, 56(1): 113-120
15 Clough RW, Penzien J. Dynamics of Structures. New York: McGraw-Hill, 1975
2 To CWS. Response statistics of discretized structures to non-stationary random processes. Journal of Soundand Vibration, 1986, 106: 217-231
3 Gasparini DA, Debchaudhury A. Response of MDOF systems to filtered non-stationary random excitation. JEgg Mech, ASCE, 1980, 106: 1233-1248
4 Perotti F. Structural response to non-stationary multi-support random excitation. Earthquake Engineering andStrvctural Dynamics. 1990. 19: 513-527
5王君杰,周晶.地震动频谱非平稳性对结构非线性反应的影响.地展工程与工程振动, 1997, 17(2): 16～20(WangJunjie, Zhou Jing. Effects of frequency nonstationarity of seismic ground motion on inelastic response ofstructure. Earthquake Enqineerinq and Engineering Vibration, 1997, 17(2): 16-20 (in Chinese))
6林家浩,张亚辉,孙东科等.受非均匀调制演变随机激励结构响应快速精确算法.计算力学学报, 1997,14(1): 2～8(LinJiahao, Zhang Yahui, Sun Dongke et al. Fast and precise computation of Structural responses to non-uniformlymodulated evolutionary random excitations. Chinese Journal of Computational Mechanica, 1997, 14(1): 2-8(in Chinese))
7林家浩.随机地震响应的确定性算法.地震工程与工程振动, 1985, 5(1): 89～94(Lin Jiahao. A deterministicalgorithm for stochastic seismic response. Earthquake Engineering cud Bngineering Vibrntion, 1985, 5(1):89-94 (in Chinese))
8 Lin Jiahao, Williams FW, Zhang Wenshou. A new approach to multiphase excitation stochastic seismic response.Microcomputers in Civil Engineering, 1993, 8: 283-290
9林家浩,李建俊,张文首.结构受多点非平稳随机地震激励的响应.力学学报,1995,27(5):567～576(Lin Jiahao,LiJianjun, Zhang Wenshou. Structural responses to nonstationary multi-point random seismic excitations. ActaMechanics Sinica, 1995, 27(5): 567-576 (in Chinese))
10 Lin Jiahao, Williams FW. Computation and analysis of multi-excitation random seismic responses. EngineeringComputotions, 1992, 9: 561-574
11 Kiureghian AD, Neuenhofer A. Response spectrum method for multi-support seismic excitations. EarthquakeEngineering and Structural Dynamics, 1989, 21: 713-740
12 Ernesto HZ, Vanmarcke EH. Seismic random vibration analysis of multi-support structural systems. J EggMech, ASCE, 1994, 120(5): 1107-1128
13钟万勰.结构动力方程的精纲时程积分方法.大连理工大学学报, 1994, 34(2): 131～136(Zhong Wanxie. Precisetime integration method for structural dynamic equations. Journal of Dalian University of Technology, 1994,34(2): 131-136 (in Chinese))
14 Lin Jiahao, Shen Weiping, Williams FW. A high precision direct integration scheme for structures subjected totransient dynamic loading. Computers and Structures, 1994, 56(1): 113-120
15 Clough RW, Penzien J. Dynamics of Structures. New York: McGraw-Hill, 1975
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