简谐波地震动反应谱研究
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摘要
简谐荷载作用下单自由度体系的动力反应是典型的结构动力学问题,也是地震工程中研究结构地震反应的基础。对简谐地震动反应谱特性的研究有利于认识地震动、尤其是近场地震动的特性以及它对结构地震反应的影响。基于结构动力学的基本理论,推导了简谐地震动作用下,单自由度体系的理论解、瞬态解和稳态解。分析了简谐地震动全解反应谱、稳态解反应谱和瞬态解反应谱的特性并讨论了它们之间的关系。研究结果表明:在简谐地面加速度作用下,高频地震动也可以引起长周期结构产生很大的位移反应,且最大位移反应出现在结构的瞬态自由振动阶段。这不仅揭示了近场地震动对结构反应的重要影响,也从另一个侧面揭示了近场地震动的潜在破坏作用,而且提出了在近场情况下结构抗震不可忽略结构的瞬态自由振动影响的观点。
The response of SDOF system to harmonic excitation is a classical topic in structural dynamics,it is also the basic theory used in earthquake engineering.Therefore,the study of response spectra to harmonic ground motion can provide some insight in the characteristics of real earthquake ground motion,particularly those generated by near-source earthquake.Based on the theory of structural dynamics,the complete solution,steady state solution and transient solution as well as their respective response spectra of SDOF systems subjected to harmonic ground motions are derived and the relations among these three kinds of response spectra are discussed.It is concluded that the transient response to a high frequency harmonic ground motion can increase greatly the displacement response of structures,particularly for the long period structures.The transient vibration should not be ignored in the earthquake-resistant design of real structures that are close to the causative faults.
The response of SDOF system to harmonic excitation is a classical topic in structural dynamics,it is also the basic theory used in earthquake engineering.Therefore,the study of response spectra to harmonic ground motion can provide some insight in the characteristics of real earthquake ground motion,particularly those generated by near-source earthquake.Based on the theory of structural dynamics,the complete solution,steady state solution and transient solution as well as their respective response spectra of SDOF systems subjected to harmonic ground motions are derived and the relations among these three kinds of response spectra are discussed.It is concluded that the transient response to a high frequency harmonic ground motion can increase greatly the displacement response of structures,particularly for the long period structures.The transient vibration should not be ignored in the earthquake-resistant design of real structures that are close to the causative faults.
引文
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[2]Hall J F,Heaton T H,Halling M W,Wald D J.Near-source ground motions and its effects on flexible buildings[J].Earthquake Spectra,1995,11(4):569~605.
[3]Mohsen Tehranizadeh,Farzaneh Hamedi.Influence of earthquake source parameters and damping on elastic response spectra for Iranian earthquakes[J].Engineering Structures,2002,24:933~943.
[4]Peng MH,Elghadamsi FE,Mohraz B.A simple procedure for constructing probabilistic response spectra[J].Earthquake Spectra,1989,5(2):393~407.
[5]Mohraz B.Recent studies of earthquake ground motion and amplification[C].Proceedings of the 10th World Conference on Earthquake Engineering,A.A.Balkema,Rotterdam,The Netherlands,1994.6695~6704.
[6]Newmark N M,Hall W J.Earthquake spectra and design[R].Earthquake Engineering Research Institute,Berkeley,California,1982.
[7]Sadek F,Mohraz B,Riley M A.Linear procedures for structures with velocity-dampers[J].Journal of Structural Engineering,ASCE,2000,128(8):887~895.
[8]谢礼立,于双久.强震观测与分析原理[M].北京:地震出版社,1982.Xie Lili,Yu Shuangjiu.The theory of strong earthquake motion measurement and analysis[M].Beijing:Seismological Press,1982.(in Chinese)
[9]Chopra Anil K.Dynamics of structures:Theory and applications to earthquake engineering[M].Prentice Hall:Englewood Cliffs,NJ,1995.
[10]胡聿贤.地震工程学[M].北京:地震出版社,1988.HuYuxian.Earthquake engineering[M].Beijing:Seismological Press,1988.(in Chinese)
[11]赵凤新,胡聿贤.地震动反应谱与相位差谱的关系[J].地震学报,1996,18(3):287~291.Zhao Fengxin,Hu Yuxian.Relations between earthquake response spectrum and phase difference spectrum[J].Atca Seismological Sinica,1996,18(3):287~291.(in Chinese)
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