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《Journal of Zhejiang University(Engineering Science)》 2007-01
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Bifurcation and catastrophe analysis of non-linear dynamic instability disaster for dam and foundation system

ZHANG Wo-hua~1,QIU Zhan-hong~(1,2),CHEN He-long~2(1.Institute of Geotechnical Engineering,Zhejiang University,Hangzhou 310027, China;2.Architecture and Civil Engineering College,Taizhou University,Taizhou 317000,China)  
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.
【Fund】: 国家自然科学基金资助项目(50379046);; 教育部博士点基金资助项目(A50221)
【CateGory Index】: TV223.31
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