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.