单自由度体系地震动力响应的混沌特性分析
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摘要
引入非线性动力学理论和混沌时间序列分析方法考察地震动作用下单自由度体系动力响应的混沌特性。输入典型近断层地震动记录,定量计算了代表性周期的单自由度弹性和非弹性体系加速度响应时程的非线性特性参数。计算表明,这些加速度响应的关联维数为分数维,最大Lyapunov指数大于0;地震动激励下单自由度体系的地震动力响应具有混沌特性,不是完全的随机信号,为理解结构地震动力响应的不规则性与复杂性提供了新思路和新视角。
Nonlinear dynamics theory and chaotic time series analysis are suggested to examine the chaotic characteristic of dynamic responses of single degree of freedom(SDOF)system subjected to earthquake ground motions in this paper.The typical near-fault ground motion records are selected as the seismic input.Then,the chaotic time series analysis is applied to calculate quantitatively the nonlinear characteristic parameters of acceleration responses of elastic and inelastic SDOF systems with representative periods.Numerical results show that the correlation dimension of these acceleration responses is fractal dimension,and their maximal Lyapunov exponent is larger than 0.Moreover,it is illustrated that the seismic dynamic responses of SDOF system under earthquake excitation present the chaotic character rather than the pure random signal,which provides us new approach and new perspective for understanding the irregularity and complexity of the seismic dynamic responses of structures.
Nonlinear dynamics theory and chaotic time series analysis are suggested to examine the chaotic characteristic of dynamic responses of single degree of freedom(SDOF)system subjected to earthquake ground motions in this paper.The typical near-fault ground motion records are selected as the seismic input.Then,the chaotic time series analysis is applied to calculate quantitatively the nonlinear characteristic parameters of acceleration responses of elastic and inelastic SDOF systems with representative periods.Numerical results show that the correlation dimension of these acceleration responses is fractal dimension,and their maximal Lyapunov exponent is larger than 0.Moreover,it is illustrated that the seismic dynamic responses of SDOF system under earthquake excitation present the chaotic character rather than the pure random signal,which provides us new approach and new perspective for understanding the irregularity and complexity of the seismic dynamic responses of structures.
引文
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[3]Huang J,Turcotte D L.Evidence for chaotic fault interaction in the seismicity of the San Andreas fault and Nakai trough[J].Nature,1990,348(2):234-236.
[4]Carlson J M,Langer J S,Shaw B E.Dynamics of earthquake faults[J].Reviews of Modern Physics,1994,66(2):657-670.
[5]Vieira M S.Chaos and synchronized chaos in an earthquake model[J].Physical Review Letters,1999,82(1):201-204.
[6]Montagne R,Vasconcelos G R.Complex dynamics in a one-block model for earthquakes[J].Physica A,2004,342(2):178-185.
[7]杨迪雄,杨丕鑫.强震地面运动的混沌特性分析[J].防灾减灾工程学报,2009,29(3):210-217.(YANG Di-xiong,YANG Pi-xin.Chaotic characteristic anal-ysis of strong earthquake ground motions[J].Journal of Disaster Prevention and Mitigation Engineering,2009,29(3):210-217.(in Chinese))
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[10]刘秉正,彭建华.非线性动力学[M].北京:高等教育出版社,2004.(LIU Bing-zheng,PENG Jian-hua.Nonlinear Dynamics[M].Beijing:Higher Education Press,2004.(in Chinese))
[11]韩敏.混沌时间序列预测理论与方法[M].北京:中国水利水电出版社,2007.(HAN Min.Prediction Theory and Method of Chaotic Time Series[M].Bei-jing:China Water Power Press,2007.(in Chinese))
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