指数型变截面桩中的纵波

Longitudinal waves in piles with exponentially varying cross sections

解析地研究了指数型变截面桩中的纵波。桩顶受到纵向冲击力作用,桩身为有限长均匀弹性圆杆,其半径按指数变化,桩周土剪切波速也按指数变化,并考虑桩土相互作用。由Laplace变换和逆变换,分别得到纵向振动的桩土系统的传递函数和脉冲响应。进一步得到桩顶纵向振动速度的频响函数、频域和时域表达式。研究了渐缩自由桩和渐扩自由桩的桩顶纵向振动速度时域曲线特征;研究了渐变截面桩的桩顶纵向振动速度时域曲线、振幅谱曲线和导纳曲线特征;结果表明:桩身截面的渐缩和渐扩都产生桩身反射波,这种桩身反射波是缓变化的,其大小与桩身截面渐变的程度正相关;桩身截面的渐变主要影响频域曲线的几个低阶共振峰。由参数研究及推出的理论公式揭示,桩中纵波的衰减取决于桩周顶部土剪切波速与桩身纵波波速比、桩长与桩顶直径比、桩周土密度与桩身密度比。

Longitudinal waves in piles with exponentially varying cross sections were analytically studied. The pile, subjected to longitudinal impact force at the top, was assumed to be a homogeneous elastic circular bar with finite length and exponentially varying radii. The velocity of shear wave in the surrounding soil was also assumed to vary exponentially, and the soil-pile interaction was taken into account. The transfer function and pulse response of the soil-pile system under longitudinal vibration were derived by direct and inverse Laplace transforms, respectively. The frequency response function, frequency-domain and time-domain expressions for the longitudinal vibration velocity at the pile top were obtained further. The characteristics of longitudinal waves for piles with gradually varying and equal cross sections were investigated. It was found that reflected waves could be produced by the gradual variation of the cross section of pile, which varied with the variation of the cross section of pile, mainly affecting the low frequency resonant peaks. It was shown by parametric studies and the proposed theoretical formula that the attenuation of longitudinal waves in the pile depended on three ratios, that is, the ratio of shear wave velocity in soil to longitudinal wave velocity in pile, the ratio of pile length to diameter of pile top, and the ratio of the soil density to the pile density.