结构-滑移基础-土非线性相互作用体系主共振与分叉
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摘要
本文基于修改后的非线性Davidenkov动力模型，采用非线性有限元得到基础与土之间的滑移刚度，从而建立了结构－滑移基础－地基土相互作用体系。用平均法研究体系的主共振，得到主共振定常解和幅频响应函数，讨论了定常解的稳定性。根据奇异性理论求得开折参数平面下的转迁集和分叉图，从分叉图出发讨论了体系的动力行为，得到了一些有益的结论。
In this paper, based on modified Davidenkov model, the nonlinear finite element method is adopted to obtain the relationship between horizontal load and displacement of foundation. The computation model of the nonlinear interaction system of structure-slide foundation-soil is derived. The method of average is used to study the primary resonance of nonlinear interaction system. The steady-state solution of the primary resonance and a function of amplitude-frequency are obtained, and the stability of solution is discussed. According to singularity theory, the transition variety and the bifurcate diagram are given on the plane of unfolding parameters. By discussing bifurcate diagram, the dynamic behavior of structure-slide foundation-soil interaction system is analyzed. Some useful conclusions have been drawn through the analyses of numerical examples.
In this paper, based on modified Davidenkov model, the nonlinear finite element method is adopted to obtain the relationship between horizontal load and displacement of foundation. The computation model of the nonlinear interaction system of structure-slide foundation-soil is derived. The method of average is used to study the primary resonance of nonlinear interaction system. The steady-state solution of the primary resonance and a function of amplitude-frequency are obtained, and the stability of solution is discussed. According to singularity theory, the transition variety and the bifurcate diagram are given on the plane of unfolding parameters. By discussing bifurcate diagram, the dynamic behavior of structure-slide foundation-soil interaction system is analyzed. Some useful conclusions have been drawn through the analyses of numerical examples.
引文
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[2] 陈予恕, 毕勤胜. 振动磨机的分段线性研究[J]. 天津大学学报, 1996, 29(1):31-38. Chen Yushu, Bi Qinsheng. Piecewise linearity research on vibratom[J]. Journal of Tianjin University, China, 1996, 29(1):31-38.
[3] 钱家欢, 殷宗泽. 土工原理与计算[M]. 中国水利水电出版社,1996. Qian Jiahuan, Yin Zongze. Principles and computation in geotechnics [M]. China Water Conservancy & Hydroelectricity Publishing Company, 1996.
[4] Golubitsky M S., Schaeffer D G. Singularties and groups in bifurcation theory[M]. New York: Springer-Verlag, 1985.
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