与黏弹性地基相互作用的单桩的自振特性分析

Analysis for Natural Vibration Characteristics of a Single Pile in Viscoelastic Foundation

将回传射线矩阵法推广至桩土系统的振动分析中,利用MATLAB语言编程,借助求根法对二维复数超越方 程进行迭代求解,通过数值算例,对比分析黏弹性地基中桩的外露长度、埋置深度、桩端约束情况对自振频率、衰减系 数和模态的影响。结果表明:随着外露长度越长,埋置结构的各阶自振频率和衰减系数越小;随着埋置深度越深,埋置 结构的各阶自振频率越小,衰减系数越大;埋置部分的横向位移明显小于外露部分的横向位移;桩顶固定边界下单桩 的各阶自振频率最大,桩顶自由边界下单桩的各阶衰减系数最小;桩顶自由工况下单桩各阶振型峰值相对其在桩顶铰 接和桩顶固定工况下的振型峰值较小。

The reverberation-ray matrix method is introduced to the vibration analysis of pile-foundation systems.The MATLAB code is used to solve the two-dimensional complex transcendental equation with the help of the root method.Through numerical examples of a pile in the viscoelastic foundation,the effects of the exposed length,the depth and the constraint condition of the pile on the natural frequency,attenuation coefficient and modals are analyzed and compared.The results show that the natural frequency and attenuation coefficient of the embedded structures decreases with the increase of the exposed length.When the buried depth decreases in the embedded structures,the natural frequency decreases and the attenuation coefficient increases.The transverse displacement of the buried part is obviously smaller than that of the exposed part.The natural frequency of the pile beneath the fixed top boundary is the largest,the attenuation coefficients of the pile beneath the free top boundary is the smallest.The vibration amplitude of the free top of the pile is smaller than that of the hinge top and the fixed top.