The Research On Nonlinear Dynamic Characteristics Of Piles

The pile foundations are widely used in engineering, such as, high-rise building, bridge, offshore platform and nuclear power station. It is very difficult to perform the nonlinear mechanical analysis, numerical simulation and experiment of piles due to the complexity of the interaction between the pile and the soil, the load transfer, deformation and motion. Although there are many papers on linear vibrations and the dynamic response of piles, there are few papers on nonlinear dynamic behaviors and nonlinear vibrations of piles, especially, both the materials of the pile and the soil are nonlinear elastic and viscoelastic ones.In the present thesis, under the assumption that both the materials of the pile and the soil around the pile are nonlinear elastic and linear viscoelastic ones, the mathematics models analyzing the nonlinear dynamic characteristics of piles are established using generalized Winkler models, and the linear and nonlinear dynamic characteristics of piles are studied using the plural mode method, the method of multiple time scales, Galerkin method, bifurcation and chaos analysis method and so on. The effects of parameters on the nonlinear dynamic characteristics of piles are considered and some new results are given.The main research contents are as follows:(1) On the basis of generalized Winkler models, the nonlinear partial differential equation governing the nonlinear vibration of piles are derived under the assumption that both the materials of the pile and the soil around the pile obey nonlinear elastic and linear viscoelastic constitutive relations, and the relevant boundary conditions and the initial conditions are given.(2) An accurate expressions of the nth-order vibration mode, the natural frequency and the displacement response of the axial and transverse vibration of piles are presented by the plural mode method. Results show that the natural frequency of the axial and transverse vibration of piles is related to not only the damping coefficient and the boundary conditions, but also the soil rigidity. (3) When both the viscidities of materials of the pile and the soil around the pile are weak and the non-linearities of materials can be neglected, the approximate expressions of the nth-order natural frequency and the displacement response of the axial vibration of piles are obtained by the method of multiple time scales with order 4. Research results show that the natural frequency is related to not only the damping coefficient, but also the soil rigidity.(4) Under the assumption that both the nonlinear characters of materials of the pile and the soil are weak, the approximate expressions of the nth-order main frequency and the displacement response of the nonlinear axial and transverse vibration of piles are obtained by the method of multiple time scales, respectively. Numerical examples are implemented and the effects of parameters are considered. Research results show that the main frequency of the nonlinear system is related to not only the natural frequency of linear vibration system, but also the amplitude, damping coefficient and nonlinearity of materials. There are high order harmonic waves with double and triple of the main frequency as well as sum and/or difference of 2 or 3 main frequencies besides the harmonic waves with the main frequency in the response of nonlinear systems.(5) Under the assumption that all the nonlinear elastic characters and the linear viscoelastic characters of materials of the pile and the soil are weak, the steady-state frequency-response curves for the primary resonances of the nonlinear axial forced vibration of piles are presented by the method of multiple time scales. The stability of the steady-state response for the primary resonances of the nonlinear system is investigated. Numerical examples are given and the effects of the material nonlinearity, the damping coefficient and the amplitude of the excitation on the frequency-response curves are considered.(6) Under the assumption that the axially periodic displacement at the top of pile is given, the nonlinear partial differential equation for motion of piles is derived under the assumption of both the materials of the pile and the soil around the pile obey nonlinear elastic and linear viscoelastic constitutive relations. The Galerkin method is used to simplify the equation and to obtain a nonlinear ordinary differential equation. The methods in nonlinear dynamics are applied to solve the simplified dynamical system, and all the time-path curves, phase-trajectory diagrams, power spectrum, Poincare sections, and bifurcation and chaos diagrams of the simplified system are obtained. The effects of parameters on the dynamic characteristics of the system are also considered in detail. Research results show that a pile embedded in rock may present different motion shapes included periodic motion, quasi-periodic motion, bifurcation or chaotic motion and so no.(7) The nonlinear transverse motion of piles embedded in rock is studied. Here, we assume that both the materials of the pile and soil obey nonlinear elastic and linear viscoelastic constitutive relations and that a transverse periodic displacement at the top of the pile is given. The initial-boundary value problem is firstly set up which is a nonlinear partial differential equation. Galerkin method is used to simplify the governing equation and to obtain a simplified dynamic system. All the time-path curves, phase-trajectory diagrams, power spectrum, Poincare sections, and bifurcation and chaos diagrams are obtained. The effects of parameters on the nonlinear characteristics are considered in detail. Research results show that a pile embedded in rock may present different motion shapes included periodic motion, quasi-periodic motion, bifurcation or chaotic motion and so no.