关键词: 非线性粘弹性桩, 纵向振动, 混沌运动, 数值计算

Abstract: The vertical chaotic motion of the nonlinear viscoelastic pile embedded in rock with a vertical displacement, is investigated. Supposing that the pile satisfied the constitutive relations of nonlinear elasticity and linear viscoelasticity, and the reacting force of soil to the pile is in direct proportion to displacement and speed rate as well as the damp. The nonlinear partial differential equation of the pile motion is obtained. Based on the Galerkin method, the equation is simplified. Moreover the numerical simulations are carried out, from which the time-path curves, phase-trajectory diagrams, power spectrums, and Poincare section and bifurcation diagrams for the motion of piles are obtained with different parameters under the following conditions, such as the reacting force and the damp of the soil, the damp of the pile comparatively big, small and very small etc.. The results show that the vertical motion of the nonlinear viscoelastic pile could present periodic, quasi-periodic, bifurcation and chaotic motion.

Key words: nonlinear viscoelastic pile, vertical vibration, chaotic motion, numerical calculation