堤坝和基础非线性动力失稳灾变的分岔突变分析
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摘要
为了更深刻本质地研究堤坝系统发生动力溃坝灾害的机理,应用非保守系统拉格朗日动力学理论建立了堤坝-基础系统在地震荷载作用下3个自由度的非线性动力学模型,它描述了堤坝-基础系统在地震荷载作用下的横向振动、竖向振动和基础振动的非线性特征.在此基础上,对由振幅、作用力和激振频率所表示的相空间中动力系统在简谐激励作用下共振响应表现出的畸变、折叠、突跳和滞后等现象,以及对在范德玻尔轨迹平面上系统稳定性分岔的特征和共振峰畸变突跳现象的机理,以及分频过程的亚谐振的现象进行了研究,从不同角度对非线性动力系统给出了双(或单)尖点突变模型,描述了由堤坝-基础结构中非线性因素演化造成系统稳定性分岔所导致的系统振幅平方A21失稳突跳抖动,使堤坝系统的动能(或动量)发生突然的改变,从而在系统内产生了很大的冲击应力的灾变机理.
In order to explain the paroxysmal disaster mechanism of dam system in dynamic debacle more constitutionally and profoundly,a nonlinear dynamic model with three degrees of freedom was constructed to express nonlinear characters of horizontal and vertical vibrations of the dam body and earthquake with the foundation based on Lagrange dynamic equations under seismic load from unconservative energy analysis of the system.The phenomena of distortion,folding,jumping and lagging in resonance with the dynamic system under harmonic excitation were taken into account by observation in the phase space,which consists of the vibration amplitude,the force and frequency of the excitation.The characters of stability bifurcation,the mechanism of distortion and the catastrophe of the resonance peak as well as the behavior of inferior harmonic vibration were expressed on the phase plane of van der Pol's orbits.Dynamic catastrophe models of the dam-foundation system with both double and single cusps were presented from different points of view,describing the stability bifurcation of the dynamic system due to the variation of nonlinear factors and causes instable sudden square amplitude A~2_1,tingles and may suddeny change the kinetic energy or kinetic moment of the system to produce very high shock stress.
In order to explain the paroxysmal disaster mechanism of dam system in dynamic debacle more constitutionally and profoundly,a nonlinear dynamic model with three degrees of freedom was constructed to express nonlinear characters of horizontal and vertical vibrations of the dam body and earthquake with the foundation based on Lagrange dynamic equations under seismic load from unconservative energy analysis of the system.The phenomena of distortion,folding,jumping and lagging in resonance with the dynamic system under harmonic excitation were taken into account by observation in the phase space,which consists of the vibration amplitude,the force and frequency of the excitation.The characters of stability bifurcation,the mechanism of distortion and the catastrophe of the resonance peak as well as the behavior of inferior harmonic vibration were expressed on the phase plane of van der Pol's orbits.Dynamic catastrophe models of the dam-foundation system with both double and single cusps were presented from different points of view,describing the stability bifurcation of the dynamic system due to the variation of nonlinear factors and causes instable sudden square amplitude A~2_1,tingles and may suddeny change the kinetic energy or kinetic moment of the system to produce very high shock stress.
引文
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[3]张楚汉.水利水电工程科学前沿[M].北京:清华大学出版社,2002:357 397.
[4]ARNOLD V I.Catastrophe theory[M].Heideberg,Berlin:Springer Verlage,1980.
[5]IDRISS I M,SEED H B.Seismic response of horizontalsoil layers[J].Journal of the Soil Mechanics and Foun-dation Division,American Society of Civil Engineers,1968,95(4):693 698.
[6]中华人民共和国国家标准编写组.建筑抗震设计规范GB50011-2001[S].北京:中国建筑工业出版社,1999.
[7]陈予恕.非线性振动系统的分叉和混沌理论[M].北京:高等教育出版社,1993.
[8]GUCKENHEIMER J,HOLMES P.Nonlinear oscilla-tions,Dynamical System and Bifurcations of vector fields[M].New York:Srringer-Verlag,1983.
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