基于地震动相位谱不确定性模型的单自由度体系响应
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摘要
提出了一个基于随机微分方程的群延时模型用以描述和模拟地震动相位谱.利用此相位谱模型推导出了线性单自由度结构体系在地震荷载作用下位移响应均值和方差的理论计算公式,采用时域和频域的方法对位移响应的统计特性进行了分析.结果表明:该相位谱模型能较好地模拟实际地震动的相位谱;对于线性单自由度体系,在任一频率处,位移响应相位角的均值与激励群延时的均值成反比;而位移响应相位角的方差与激励群延时的方差成正比;位移响应的均值和方差均与激励各谐波分量相位角的方差成反比,从而位移响应的峰值亦与该方差成反比.
A group delay time(GDT) model is presented to characterize and simulate phase spectrum of ground motion by using stochastic differential equation(SDE).Based on the GDT model,theoretical equations were founded to calculate mean and variance of displacement response of single degree of freedom(SDOF) system under earthquake loads.Statistical characteristics of system displacement response were clarified by using analysis both in time domain and in frequency domain.The results show that the phase spectrum model proposed can provide efficient simulations of real ground motions.For SDOF system,mean value of phase angle of displacement response is inversely proportional to mean value of GDT of excitation at each frequency,while variance of phase angle of displacement response is directly proportional to variance of GDT of excitation.The mean and variance of displacement response of SDOF system get large when variances of phase angle of exciting harmonic waves become small.And so does the peak displacement response.
A group delay time(GDT) model is presented to characterize and simulate phase spectrum of ground motion by using stochastic differential equation(SDE).Based on the GDT model,theoretical equations were founded to calculate mean and variance of displacement response of single degree of freedom(SDOF) system under earthquake loads.Statistical characteristics of system displacement response were clarified by using analysis both in time domain and in frequency domain.The results show that the phase spectrum model proposed can provide efficient simulations of real ground motions.For SDOF system,mean value of phase angle of displacement response is inversely proportional to mean value of GDT of excitation at each frequency,while variance of phase angle of displacement response is directly proportional to variance of GDT of excitation.The mean and variance of displacement response of SDOF system get large when variances of phase angle of exciting harmonic waves become small.And so does the peak displacement response.
引文
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[3]Yamane T,Nagahashi S.A study on a generation ofsimulated earthquake ground motion considering phasedifference characteristics[J].Journal of Structural andConstruction Engineering,2010,75(649):539-548.
[4]Katsukura K,Izumi M.A foundamental study on thephase properties of seismic w aves[J].Journal ofStructural and Construction Engineering,Transactionsof AIJ,1983,327(5):20-27.
[5]Sato T,Murono Y,Nishimura A.Phase spectrum mod-eling to simulate design earthquake motion[J].Journalof Natural Disaster Science,2002,24(2):91-100.
[6]Zhang Cong,Sato T,Lu Lingyi.A phase model ofearthquake motions based on stochastic differentialequation[J].KSCE Journal of Civil Engineering,2011,15(1):161-166.
[7]Boore D M.Phase derivatives and simulation of strongground motions[J].Bulletin of the Seismological Soci-ety of America,2003,93(3):1132-1143.
[8]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.
[9]Murono Y.Evaluation of response spectrum consideringthe stochastic characteristics of the phase spectrum ofearthquake motion[J].Quarterly Report of RTRI,2008,49(2):85-88.
[10]Mikosch Thomas.Elementary stochastic calculus withfinance in view[M].Singapore:World ScientificPublishing Co.Pte.Ltd,1998.
[2]田玉基,杨庆山.基于相位差谱的空间相关非平稳地震动场的模拟[J].计算力学学报,2010,27(5):828-833.Tian Yuji,Yang Qingshan.Phase-difference-based sim-ulation of spatial correlated and non-stationary seismicground motions[J].Chinese Journal of ComputationalMechanics,2010,27(5):828-833.(in Chinese)
[3]Yamane T,Nagahashi S.A study on a generation ofsimulated earthquake ground motion considering phasedifference characteristics[J].Journal of Structural andConstruction Engineering,2010,75(649):539-548.
[4]Katsukura K,Izumi M.A foundamental study on thephase properties of seismic w aves[J].Journal ofStructural and Construction Engineering,Transactionsof AIJ,1983,327(5):20-27.
[5]Sato T,Murono Y,Nishimura A.Phase spectrum mod-eling to simulate design earthquake motion[J].Journalof Natural Disaster Science,2002,24(2):91-100.
[6]Zhang Cong,Sato T,Lu Lingyi.A phase model ofearthquake motions based on stochastic differentialequation[J].KSCE Journal of Civil Engineering,2011,15(1):161-166.
[7]Boore D M.Phase derivatives and simulation of strongground motions[J].Bulletin of the Seismological Soci-ety of America,2003,93(3):1132-1143.
[8]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.
[9]Murono Y.Evaluation of response spectrum consideringthe stochastic characteristics of the phase spectrum ofearthquake motion[J].Quarterly Report of RTRI,2008,49(2):85-88.
[10]Mikosch Thomas.Elementary stochastic calculus withfinance in view[M].Singapore:World ScientificPublishing Co.Pte.Ltd,1998.
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