基于瞬时输入能量时变特征的SDOF体系位移历程模拟
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摘要
目前地震能量分析方法的研究多集中于对结构总输入能与总滞回耗能的简化估计,忽略了能量沿时间轴输入历程的不同所导致的结构反应的差别。该文以瞬时输入能量在时间轴上的分布特征(瞬时输入能量时变特征)来描述地震能量输入历程的特点,并通过建立瞬时输入能量时变特征与结构位移历程之间的联系,获得了基于能量参数的结构位移历程求解方法。为验证该方法的准确性,采用最大位移值和等效循环次数两个指标分别进行比较,分析表明,该方法在模拟弹性结构的幅值反应和持时反应上具有较好的准确性。该模型的获得将为基于能量概念的弹塑性结构损伤历程研究提供必要的基础。
Currently,analytical methods based on seismic energy of structures mainly focused on the simplified estimation approach of input energy and hysteretic energy.As a result,the response of structures can't reflect the effect of time-frequency characteristics of earthquake energy.A mathematical model is proposed in this paper to reflect the time varying characteristic of momentary input energy.By establishing the relationship between the time varying characteristic of momentary input energy and the deformation history of a linear single degree of freedom(SDOF) system,the paper developed a simplified procedure to simulate the deformation history,which was validated using the maximum deformation and cyclic demand spectrum of a linear system.It is found that the simulated deformation response can reflect the max amplitude of actual deformation and the effect of duration.This research provided theoretical foundation for the study on the simulated deformation history and the quantization of cumulative damage.
Currently,analytical methods based on seismic energy of structures mainly focused on the simplified estimation approach of input energy and hysteretic energy.As a result,the response of structures can't reflect the effect of time-frequency characteristics of earthquake energy.A mathematical model is proposed in this paper to reflect the time varying characteristic of momentary input energy.By establishing the relationship between the time varying characteristic of momentary input energy and the deformation history of a linear single degree of freedom(SDOF) system,the paper developed a simplified procedure to simulate the deformation history,which was validated using the maximum deformation and cyclic demand spectrum of a linear system.It is found that the simulated deformation response can reflect the max amplitude of actual deformation and the effect of duration.This research provided theoretical foundation for the study on the simulated deformation history and the quantization of cumulative damage.
引文
[1]Kunnath S K,Chai Y H.Cumulative damage-based inelastic cyclic demand spectrum[J].Earthquake Engineering&Structural Dynamics,2004,33(6):499―520.
[2]Iunio Iervolino,Gaetano Manfredi,Edoardo Cosenza.Ground motion duration effects on nonlinear seismic response[J].Earthquake Engineering&Structural Dynamics,2006,35(1):21―38.
[3]Fajfar P,Vidic T.Consistent inelastic design spectra:hysteretic and input energy[J].Earthquake Engineering&Structural Dynamics,1994,23(5):523―538.
[4]Chai YH,Fajfar P.A procedure for estimating input energy spectra for seismic design[J].Journal of Earthquake Engineering,2000,4(4):539―561.
[5]程光煜,叶列平.弹塑性SDOF系统的地震输入能量谱[J].工程力学,2008,25(2):28―39.Cheng Guangyu,Ye Lieping.Earthquake input energy spectrum for inelastic SDOF systems[J].Engineering Mechanics,2008,25(2):28―39.(in Chinese)
[6]刘哲锋,沈蒲生,胡习兵.地震总输入能量与瞬时输入能量谱的研究[J].地震工程与工程振动,2006,26(6):31―36。Liu Zhefeng,Shen Pusheng,Hu Xibing.Study on input energy and momentary input energy spectra of earthquake strong motion[J].Earthquake Engineering and Engineering Vibration,2006,26(6):31―36.(in Chinese)
[7]周云,乐登,邓雪松.设计用地震动总输入能量谱研究[J].工程抗震与加固改造,2008,30(5):1―7.Zhou Yun,Yue Deng,Deng Xuesong.Research on input energy spectra for design of earthquake strong motion[J].Earthquake Resistant Engineering and Retrofitting,2008,30(5):1―7.(in Chinese)
[8]曹晖,林学鹏.地震动非平稳特性对结构非线性响应影响的分析[J].工程力学,2006,23(12):30―35.Cao Hui,Lin Xuepeng.The effect of nonstationary chaeacteristic of earthquake ground motion on the structural nonlinear response[J].Engineering Mechanics,2006,23(12):30―35.(in Chinese)
[9]Norio Hori,Norio Inoue.Damaging properties of ground motions and prediction of maximum response of structures based on momentary energy response[J].Earthquake Engineering&Structural Dynamics,2002,31(3):1657―1679.
[10]胡冗冗,王亚勇.地震动瞬时能量与结构最大位移反应关系研究[J].建筑结构学报,2000,5(1):71―76.Hu Rongrong,Wang Yayong.A study on relation of instantaneous energy of earthquake strong motion and maximum displacement response of structures[J].Journal of Building Structures,2000,5(1):71―76.(in Chinese)
[11]施金龙,吕洁.应用统计学[M].南京:南京大学出版社,2005.Shi Jinlong,Lu Jie.Applied statistics[M].Nanjin:Nanjin University Publishing House,2005.(in Chinese)
[12]Sucuoglu H,Nurtug A.Prediction of seismic energy dissipation in SDOF systems[J].Earthquake Engineering&Structural Dynamics,1995,24(2):1215―1223.
[13]Malhotra P K.Cyclic-demand spectrum[J].Earthquake Engineering&Structural Dynamics,2002,31(6):1441―1457.
[2]Iunio Iervolino,Gaetano Manfredi,Edoardo Cosenza.Ground motion duration effects on nonlinear seismic response[J].Earthquake Engineering&Structural Dynamics,2006,35(1):21―38.
[3]Fajfar P,Vidic T.Consistent inelastic design spectra:hysteretic and input energy[J].Earthquake Engineering&Structural Dynamics,1994,23(5):523―538.
[4]Chai YH,Fajfar P.A procedure for estimating input energy spectra for seismic design[J].Journal of Earthquake Engineering,2000,4(4):539―561.
[5]程光煜,叶列平.弹塑性SDOF系统的地震输入能量谱[J].工程力学,2008,25(2):28―39.Cheng Guangyu,Ye Lieping.Earthquake input energy spectrum for inelastic SDOF systems[J].Engineering Mechanics,2008,25(2):28―39.(in Chinese)
[6]刘哲锋,沈蒲生,胡习兵.地震总输入能量与瞬时输入能量谱的研究[J].地震工程与工程振动,2006,26(6):31―36。Liu Zhefeng,Shen Pusheng,Hu Xibing.Study on input energy and momentary input energy spectra of earthquake strong motion[J].Earthquake Engineering and Engineering Vibration,2006,26(6):31―36.(in Chinese)
[7]周云,乐登,邓雪松.设计用地震动总输入能量谱研究[J].工程抗震与加固改造,2008,30(5):1―7.Zhou Yun,Yue Deng,Deng Xuesong.Research on input energy spectra for design of earthquake strong motion[J].Earthquake Resistant Engineering and Retrofitting,2008,30(5):1―7.(in Chinese)
[8]曹晖,林学鹏.地震动非平稳特性对结构非线性响应影响的分析[J].工程力学,2006,23(12):30―35.Cao Hui,Lin Xuepeng.The effect of nonstationary chaeacteristic of earthquake ground motion on the structural nonlinear response[J].Engineering Mechanics,2006,23(12):30―35.(in Chinese)
[9]Norio Hori,Norio Inoue.Damaging properties of ground motions and prediction of maximum response of structures based on momentary energy response[J].Earthquake Engineering&Structural Dynamics,2002,31(3):1657―1679.
[10]胡冗冗,王亚勇.地震动瞬时能量与结构最大位移反应关系研究[J].建筑结构学报,2000,5(1):71―76.Hu Rongrong,Wang Yayong.A study on relation of instantaneous energy of earthquake strong motion and maximum displacement response of structures[J].Journal of Building Structures,2000,5(1):71―76.(in Chinese)
[11]施金龙,吕洁.应用统计学[M].南京:南京大学出版社,2005.Shi Jinlong,Lu Jie.Applied statistics[M].Nanjin:Nanjin University Publishing House,2005.(in Chinese)
[12]Sucuoglu H,Nurtug A.Prediction of seismic energy dissipation in SDOF systems[J].Earthquake Engineering&Structural Dynamics,1995,24(2):1215―1223.
[13]Malhotra P K.Cyclic-demand spectrum[J].Earthquake Engineering&Structural Dynamics,2002,31(6):1441―1457.
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