Research On Nonlinear Vibration Of Piles By Method Of Multiple Time Scales

With the development of economy, there are more and more large-scale bridges,harbors and tall buildings will be built in China, the piles of them are more and more complex, the requirements on earthquake-resistance are also more and more strict. Different to the beam in air,the pile is in soil, the effect that soil impose on the pile can not be ignored, the existence of resisting force and frictional resistance which soil impose on the pile limites the vibration of the pile, improve its bearing capacity. Whether the soil around pile is hard or soft impact greatly on the bearing capacity of the pile. Method of perturbation is a effective method of studing weak nonlinear system, method of multiple time scales is one of singular perturbation methods, on the basis of summarizing existing interaction soil-pile,vibration of pile and their research techiques, The axial and transverse nonlinear vibration of pile are studied by complex modal analysis method and method of multiple time scales in the paper. The main research efforts and concusions are as follows:(1) The engineering background and research significance are disscussed, the present state of research on pile-soil dynamics, vibration of the pile and analytical method are summarized and analyzed. Taking the free vibration equation of the duffing system as an example, the conception of method of multiple time scales, problem solving method and steps are mainly introduced.(2) Under the assumption that both the materials of the pile and the soil around the pile obey nonlinear elastic and linear viscoelastic constitutive relations. The nonlinear partial differential equation governing the nonlinear axial vibration of piles was derived. When the nonlinear factors are neglected, the exact solutions of the vibration modal and the natural frequency that responsing to the axial free vibration of linear viscoelastic pile are obtained by complex modal method, numerical examples were given, following conclusions can be got: nth step natural frequency is related to damping ratio, axial stiffness coefficient of the soil around pile, material Young's modulus of pile, and axial stiffness coefficient of the soil around pile impact greatly on the nth -step natural frequency. Considering the nonlinear factors, in the case that the nonlinear characters of materials of the pile and the soil are both weak,...