Analytic prediction of chaotic vibration of piles during axial vibration

Suppose that a pile embedded in rock obeys a constitutive relation of nonlinear elasticity and linear viscoelasticity, and that the soil around the pile is nonlinear elastic and linear viscoelastic constitutive relation, too. The partial differential equation analyzing the nonlinear axial vibration of the pile is first derived. The Galerkin method is used to simplify the equation. The conditions that the system has homoclinic orbit or heteroclinic orbit are given, and the parameter equations of homoclinic orbit are solved. Using the Melnikov function, the forecasting formula that the system enters chaotic states is given. The effects of the material nonlinearity, the damping coefficient, the amplitude and frequency of the excitation on the chaotic vibration of piles are considered.