【作者】 陈中学；

【导师】 胡春林；

【作者基本信息】 武汉理工大学 ， 岩土工程， 2006， 硕士

【摘要】 随着国民经济的快速发展，我国特大桥梁、港口、高层建筑越来越多，规模越来越大，基桩也越来越复杂，对抗震设计的要求也越来越高，相应地对基桩非线性振动的研究更为紧迫。与空气介质中的梁不同，基桩存在于土介质中，土介质对于基桩的作用是不能忽视的。由于土体抗力、摩阻力的存在，限制了基桩的振动，提高了基桩的承载力，土体的软硬程度对基桩的承载力有较大影响。摄动法是研究弱非线性系统的有效方法，多时间尺度法是奇异摄动法的一种。本文在分析总结现有的桩-土动力学、基桩振动及其分析方法的基础上，用复模态分析方法和多时间尺度法分析了基桩的轴向和横向非线性振动问题，主要研究工作及结论如下： (1)论述了基桩线性及非线性振动问题研究的工程背景及研究意义，总结和分析了国内外桩-土动力学、基桩振动及其分析方法的研究现状。以达芬系统的自由振动方程为例，重点介绍了多时间尺度法的概念、解题方法及步骤。 (2)假定基桩及桩周土的材料满足非线性弹性和线性粘弹性本构关系，导出了分析基桩轴向振动的非线性偏微分方程。忽略非线性因素，用复模态分析方法得到了线性粘弹性基桩轴向自由振动的振动模态和固有频率的精确解，并进行了算例分析得到：n阶固有频率与阻尼比、桩周土的轴向刚度系数、基桩材料弹性模量有关。桩周土的轴向刚度系数对基桩n阶固有频率的影响较大；考虑非线性因素，在基桩和土的非线性都比较弱的情况下，用多时间尺度法得到了一端固定、另一端自由的基桩非线性轴向自由振动的n-阶固有频率和相应于n-阶模态的位移的近似表达式，并给出了算例，考察了参数的影响。运用数学软件Mathematica编程序进行公式推导，大大简化了手工计算量。运用数学软件Matlab编程绘图得到时程曲线、振幅与频率的关系曲线、不同时刻频率比与振幅的关系曲线等。 (3)先假定基桩及桩周土的材料满足非线性弹性和线性粘弹性本构关系，导出了分析基桩横向振动的偏微分方程。忽略非线性因素，再用复模态分析方法，得到粘弹性线性基桩横向自由振动的振动模态及固有频率的精确解。根据n阶固有频率的表达式导出了基桩在土介质作用下的临界承载力公式。基桩在土介质作用下的临界承载力分为两部分，即在无土介质情况下的桩的承载力(与材更多还原

【Abstract】 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,更多还原