地震动非平稳性对大跨度空间结构随机地震响应的影响
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摘要
为了进一步完善大跨度空间结构的随机地震响应分析理论,提出了一种简便的、近似计算非平稳地震激励下结构峰值响应均值的算法,数值模拟了某体育馆大型网壳结构在平稳和非平稳地震激励下的随机地震响应.研究表明,考虑地震动的非平稳性后,各杆件的峰值响应会有不同程度的减小,约7.51%～23.3%;同时考虑行波效应和地震动非平稳性时,在地震激励的初期阶段,结构响应方差会发生变化,但不会给结构的峰值响应均值带来明显差异;不同地面视波速时,峰值响应均值的减小程度不同.由此得出,所提出的近似算法能够大幅度地减少大跨度空间结构随机地震响应分析的计算量;对于大跨度空间结构的随机地震响应分析,尤其当结构的阻尼比和自振频率很低时应考虑地震动的非平稳性;在分析地震动非平稳性的影响时,应同时考虑地震动的行波效应.
In order to perfect the theory of random seismic response analysis for long-span spatial structures,a simple approximate algorithm to calculate mean values of peak responses was presented for structures subject to nonstationary random ground excitations.The random seismic responses of a large reticulated shell structure of a gymnasium were numerically simulated for stationary and nonstationary cases.It was found that when considering nonstationarity of earthquake ground motiont,he random seismic response of each member was reduced differently by about 7.51%—23.3%.When wave passage effect and the nonstationarity were taken into account simultaneouslyt,he variances of structural responses would vary in the early short period of the earthquake,but it could not make the mean values of peak responses different significantly.The reduction of the mean values of peak responses may be different due to various apparent wave velocities.Conclusions are given that the proposed approximate algorithm can reduce the computation quantity for the random seismic response analysis of long-span spatial structures.The nonstationarity of earthquake ground motion must be considered in the analysis,especially when damping ratios and natural vibration frequencies of structures are very low.And the wave passage effect of earthquake ground motion should be considered simultaneously when analyzing the influence of nonstationarity of earthquake ground motion.
In order to perfect the theory of random seismic response analysis for long-span spatial structures,a simple approximate algorithm to calculate mean values of peak responses was presented for structures subject to nonstationary random ground excitations.The random seismic responses of a large reticulated shell structure of a gymnasium were numerically simulated for stationary and nonstationary cases.It was found that when considering nonstationarity of earthquake ground motiont,he random seismic response of each member was reduced differently by about 7.51%—23.3%.When wave passage effect and the nonstationarity were taken into account simultaneouslyt,he variances of structural responses would vary in the early short period of the earthquake,but it could not make the mean values of peak responses different significantly.The reduction of the mean values of peak responses may be different due to various apparent wave velocities.Conclusions are given that the proposed approximate algorithm can reduce the computation quantity for the random seismic response analysis of long-span spatial structures.The nonstationarity of earthquake ground motion must be considered in the analysis,especially when damping ratios and natural vibration frequencies of structures are very low.And the wave passage effect of earthquake ground motion should be considered simultaneously when analyzing the influence of nonstationarity of earthquake ground motion.
引文
[1]胡聿贤.地震工程学[M].北京:地震出版社,2006.Hu Yuxian.Earthquake Engineering[M].Beijing:Earthquake Press,2006(in Chinese).
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[7]丁阳,林伟,李忠献.大跨度空间结构多点多维非平稳随机地震反应分析[J].工程力学,2007,24(3):97-103.Ding Yang,Lin Wei,Li Zhongxian.Non-stationary ran-dom seismic analysis of long-span spatial structures un-der multi-support and multi-dimensional earthquake exci-tations[J].Engineering Mechanics,2007,24(3):97-103(in Chinese).
[8]Davernport A G.Note on the distribution of the largest value of a random function with application to gust load-ing[J].Pro Inst Civil Eng,1961,28:187-196.
[9]Lin Jiahao,Li Jianjun,Zhang Wenshou,et al.Non-stationary random seismic responses of multi-support structures in evolutionary inhomogeneous random fields[J].Earthquake Engineering and Structural Dynamics,1997,26:135-145.
[10]江近仁,洪峰.功率谱与反应谱的转换和人造地震波[J].地震工程与工程振动,1984,4(3):1-10.Jiang Jinren,Hong Feng.Conversion between power spectrum and response spectrum and artificial earth-quakes[J].Earthquake Engineering and Engineering Vibration,1984,4(3):1-10(in Chinese).
[11]Clough R W,Penzien J.Dynamics of Structures[M].3rd ed.Berkeley,CA:Computers and Structures,2004.
[2]Lin Jiahao,Shen Weiping,Williams F W.Accurate high-speed computation of non-stationary random structural response[J].Engineering Structures,1997,19(7):586-593.
[3]Lin Jiahao,Wang Xicheng,Williams F W.Asynchronous parallel computing of structural non-stationary random seismic responses[J].International Journal for Nu-merical Methods in Engineering,1997,40(12):2133-2148.
[4]赵岩,林家浩,唐光武.行波效应下结构非平稳随机地震峰值响应分析[J].力学季刊,2004,25(2):201-207.Zhao Yan,Lin Jiahao,Tang Guangwu.Peak-value res-ponses of structures subjected non-stationary differential random ground excitations[J].Chinese Quarterly of Mechanics,2004,25(2):201-207(in Chinese).
[5]Allam Said M,Datta T K.Seismic response of a cable-stayed bridge deck under multi-component non-stationary random ground motion[J].Earthquake Engineering and Structural Dynamics,2004,33(3):375-393.
[6]曹资,薛素铎.空间结构抗震理论与设计[M].北京:科学出版社,2005.Cao Zi,Xue Suduo.Seismic Analysis and Design of Spa-tial Structures[M].Beijing:Science Press,2005(in Chinese).
[7]丁阳,林伟,李忠献.大跨度空间结构多点多维非平稳随机地震反应分析[J].工程力学,2007,24(3):97-103.Ding Yang,Lin Wei,Li Zhongxian.Non-stationary ran-dom seismic analysis of long-span spatial structures un-der multi-support and multi-dimensional earthquake exci-tations[J].Engineering Mechanics,2007,24(3):97-103(in Chinese).
[8]Davernport A G.Note on the distribution of the largest value of a random function with application to gust load-ing[J].Pro Inst Civil Eng,1961,28:187-196.
[9]Lin Jiahao,Li Jianjun,Zhang Wenshou,et al.Non-stationary random seismic responses of multi-support structures in evolutionary inhomogeneous random fields[J].Earthquake Engineering and Structural Dynamics,1997,26:135-145.
[10]江近仁,洪峰.功率谱与反应谱的转换和人造地震波[J].地震工程与工程振动,1984,4(3):1-10.Jiang Jinren,Hong Feng.Conversion between power spectrum and response spectrum and artificial earth-quakes[J].Earthquake Engineering and Engineering Vibration,1984,4(3):1-10(in Chinese).
[11]Clough R W,Penzien J.Dynamics of Structures[M].3rd ed.Berkeley,CA:Computers and Structures,2004.
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