结构-滑移基础-土非线性相互作用体系主共振与分叉

PRIMARY RESONANCE AND BIFURCATION OF THE NONLINEAR INTERACTION SYSTEM OF STRUCTURE-SLIDE FOUNDATION -SOIL

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.