| At present, civil engineering construction is at high tide the time in our country. The quantity of using pile foundation in the project in our country is growing day by day every year. The pile foundation design and the construction level relate the building directly the design level and the project quality question, therefore strengthening the pile foundation design and the construction theory research appears especially importantly. If the load which affect on the pile foundation divides into the static load and dynamic load, then the key point and the difficulty of this article studying will lie in the pile foundation vibration characteristic which on the dynamic load. The pile foundation and the pile week soil phase interaction on the dynamic load have formed the complex non-linear dynamics system. Because non-linear dynamics system extremely complex and the experimental difficulty is big, the reliability guaranteed with difficulty. Since long ago, the people mainly depend on the qualitative analysis, the simplification numerical analysis and the rule of thumb to solve this kind of problem. The analysis computation precision is very low, which can not but revise gradually through the massive scenes or the construction to obtain the correct design proposal and the job practice. The actual expenditure price is very big, until now some many questions have not been solved extremely. Therefore, the research of non-linear dynamic response of pile foundation, regardless of which is the fundamental research or the engineering design application, has the extremely significant significance. This article which is on foundation of summarizing the predecessor research results utilizes mathematics, soil dynamics, structural dynamics, and mechanics of vibrations to study some questions of non-linear dynamic response of pile foundation .The main research efforts and concusions are as follows:(1)The engineering background and research significance are discussed and the present state of research on pile-soil dynamics, vibration of the pile and analytical method are summarized and analyzed.(2) The Winkle foundation beam elementary knowledge and the application in dynamic analysis of pile foundation are introduced which provides the reference for the studying of non-linear dynamic response of single pile which is under the axial cyclic load.(3)Based on a certain assumptions and the improved dynamic beam-on-Winkler's foundation model, a simplified analytic method for computing the vertical dynamic harmonic response of single pile embedded in nonhomogeneous soil layers are established by using the principle of soil dynamics and structural dynamics. The soil layers around pile are simultaneously taken into account in the proposed computational method. Finally the parametric studies are made to examine the effects of main relevant parameters on dynamic response of single pile embedded in nonhomogeneous layered soils.(4)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. |